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

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, 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, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset: 0

Author

Reinhard Zumkeller, Feb 05 2012

Keywords

• nonn

Comments

a(n) = A206245(n) for n <= 120, a(n) < A206245(n) for n > 120.

Examples

			a(12)=2 is the first nontrivial term, from the partitions 12 = 1+1+...+1 = 11+1. - _N. J. A. Sloane_, Jul 26 2017
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Repunit
• Wikipedia, Repunit
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000041, A002275, A179051.

Programs

Haskell

a206244 = p $ tail a002275_list where
   p _             0 = 1
   p rus'@(ru:rus) n = if n < ru then 0 else p rus' (n - ru) + p rus n

Mathematica

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 *)

Formula

G.f.: Product_{k>=1} 1/(1 - x^((10^k-1)/9)). - Ilya Gutkovskiy, Jul 26 2017