A141271 Number of partitions of n into nonzero Mancala numbers (A007952).

1, 1, 2, 2, 3, 4, 4, 5, 7, 8, 10, 12, 13, 16, 19, 21, 25, 29, 32, 38, 44, 49, 56, 63, 70, 80, 90, 99, 112, 125, 138, 155, 172, 189, 210, 232, 254, 282, 310, 338, 373, 409, 446, 490, 534, 580, 636, 691, 749, 818, 887, 960, 1044, 1129, 1220, 1323, 1427, 1539

Offset

1,3

Links

Table of n, a(n) for n=1..58.

Example

a(8)=#{5+3,5+1+1+1,3+3+1+1,3+1+1+1+1+1,1+1+1+1+1+1+1+1}=5;
a(9)=#{9,5+3+1,5+1+1+1+1,3+3+3,3+3+1+1+1,3+1+1+1+1+1+1,1+1+1+1+1+1+1+1+1}=7;
a(10)=#{9+1,5+5,5+3+1+1,5+1+1+1+1+1,3+3+3+1,3+3+1+1+1+1,3+1+1+1+1+1+1+1,1+1+1+1+1+1+1+1+1+1}=8.

Mathematica

lim=50; f[n_] := Fold[#2*Floor[#1/#2 + 1] &, n, Reverse@ Range[n - 1]]; a007952=Array[f, lim]; a[n_]:=Length[Select[IntegerPartitions[n], ContainsOnly[#, a007952]&]]; Array[a, lim] (* James C. McMahon, Jul 19 2025 *)

Crossrefs

Cf. A000041, A000607, A007952, A141272.

Sequence in context: A029041 A112582 A104648 * A097793 A015742 A015754

Adjacent sequences: A141268 A141269 A141270 * A141272 A141273 A141274

Keyword

nonn

Author

Reinhard Zumkeller, Jun 21 2008

Status

approved