A357454 Number of partitions of n into pentanacci numbers 1,2,4,8,16,31, ... (A001591).

1, 1, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 20, 20, 26, 26, 36, 36, 46, 46, 60, 60, 74, 74, 94, 94, 114, 114, 140, 140, 166, 167, 202, 203, 238, 240, 284, 286, 330, 334, 390, 394, 450, 456, 524, 530, 598, 608, 692, 702, 786, 800, 900, 914, 1014, 1034

Offset: 0

Author

Ilya Gutkovskiy, Sep 29 2022

Keywords

• nonn

Crossrefs

Cf. A001591, A003107, A240844, A288120, A357452, A357455.

Programs

Mathematica

A001591[0] = A001591[1] = A001591[2] = A001591[3] = 0; A001591[4] = 1; A001591[n_] := A001591[n] = A001591[n - 1] + A001591[n - 2] + A001591[n - 3] + A001591[n - 4] + A001591[n - 5]; nmax = 55; CoefficientList[Series[Product[1/(1 - x^A001591[k]), {k, 5, 20}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=5} 1 / (1 - x^A001591(k)).