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

Author

Reinhard Zumkeller, Jun 21 2008

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A000041, A000607, A007952, A141272.

Programs

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 *)