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%I #20 Jul 26 2017 10:19:06
%S 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 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 7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8
%N Number of partitions of n into repunits (A002275).
%C a(n) = A206245(n) for n <= 120, a(n) < A206245(n) for n > 120.
%H Reinhard Zumkeller, <a href="/A206244/b206244.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Repunit">Repunit</a>
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} 1/(1 - x^((10^k-1)/9)). - _Ilya Gutkovskiy_, Jul 26 2017
%e 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 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 (Haskell)
%o a206244 = p $ tail a002275_list where
%o p _ 0 = 1
%o p rus'@(ru:rus) n = if n < ru then 0 else p rus' (n - ru) + p rus n
%Y Cf. A000041, A002275, A179051.
%K nonn
%O 0,12
%A _Reinhard Zumkeller_, Feb 05 2012
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