cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A206244 Number of partitions of n into repunits (A002275).

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%I A206244 #21 Feb 16 2025 08:33:16
%S A206244 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,4,
%T A206244 4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,
%U A206244 7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8
%N A206244 Number of partitions of n into repunits (A002275).
%C A206244 a(n) = A206245(n) for n <= 120, a(n) < A206245(n) for n > 120.
%H A206244 Reinhard Zumkeller, <a href="/A206244/b206244.txt">Table of n, a(n) for n = 0..1000</a>
%H A206244 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repunit.html">Repunit</a>
%H A206244 Wikipedia, <a href="http://en.wikipedia.org/wiki/Repunit">Repunit</a>
%H A206244 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A206244 G.f.: Product_{k>=1} 1/(1 - x^((10^k-1)/9)). - _Ilya Gutkovskiy_, Jul 26 2017
%e A206244 a(12)=2 is the first nontrivial term, from the partitions 12 = 1+1+...+1 = 11+1. - _N. J. A. Sloane_, Jul 26 2017
%t A206244 With[{nn = 50}, Table[Count[IntegerPartitions@ n, k_ /; ContainsAll[Array[Floor[10^#/9] &, IntegerLength[nn + 1]], Union@ k]], {n, 0, nn}]] (* _Michael De Vlieger_, Jul 26 2017 *)
%o A206244 (Haskell)
%o A206244 a206244 = p $ tail a002275_list where
%o A206244    p _             0 = 1
%o A206244    p rus'@(ru:rus) n = if n < ru then 0 else p rus' (n - ru) + p rus n
%Y A206244 Cf. A000041, A002275, A179051.
%K A206244 nonn
%O A206244 0,12
%A A206244 _Reinhard Zumkeller_, Feb 05 2012