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

0,12

Comments

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

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000041, A002275, A179051.

Sequence in context: A300287 A226764 A344420 * A206245 A064458 A125891

Adjacent sequences: A206241 A206242 A206243 * A206245 A206246 A206247

Keyword

nonn

Author

Reinhard Zumkeller, Feb 05 2012

Status

approved