DigitCount[1, b] == {1, Subscript[s, 1], \[Ellipsis], Subscript[s, b - 2], Subscript[s, b - 1]} /; Subscript[s, 1] == \[Ellipsis] == Subscript[s, b - 2] == Subscript[s, b - 1] == 0

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> { </mo> <mrow> <mrow> <msubsup> <mi> s </mi> <mi> b </mi> <mrow> <mo> ( </mo> <mn> 1 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msubsup> <mi> s </mi> <mi> b </mi> <mrow> <mo> ( </mo> <mn> 2 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <msubsup> <mi> s </mi> <mi> b </mi> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msubsup> <mi> s </mi> <mi> b </mi> <mrow> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mn> 0 </mn> <mo> ) </mo> </mrow> </mrow> <mo> } </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <msub> <mi> s </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <msub> <mi> s </mi> <mrow> <mi> b </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> <mo> , </mo> <msub> <mi> s </mi> <mrow> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <msub> <mi> s </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <mo> &#8230; </mo> <mo> &#10869; </mo> <msub> <mi> s </mi> <mrow> <mi> b </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> <mo> &#10869; </mo> <msub> <mi> s </mi> <mrow> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <list> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> s </ci> <ci> b </ci> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> s </ci> <ci> b </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <ci> &#8230; </ci> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> s </ci> <ci> b </ci> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> s </ci> <ci> b </ci> </apply> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 0 </cn> </apply> </list> <list> <cn type='integer'> 1 </cn> <apply> <ci> Subscript </ci> <ci> s </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> s </ci> <apply> <plus /> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> s </ci> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> </list> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> s </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> s </ci> <apply> <plus /> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> s </ci> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DigitCount", "[", RowBox[List["1", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List["1", ",", SubscriptBox["s", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["s", RowBox[List["b", "-", "2"]]], ",", SubscriptBox["s", RowBox[List["b", "-", "1"]]]]], "}"]], "/;", RowBox[List[SubscriptBox["s", "1"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["s", RowBox[List["b", "-", "2"]]], "\[Equal]", SubscriptBox["s", RowBox[List["b", "-", "1"]]], "\[Equal]", "0"]]]]]]]]

2001-10-29