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A357519
Number of compositions (ordered partitions) of n into Jacobsthal numbers 1,3,5,11,21,43, ... (A001045).
0
1, 1, 1, 2, 3, 5, 8, 12, 19, 30, 47, 75, 118, 185, 292, 460, 725, 1143, 1800, 2836, 4469, 7042, 11097, 17485, 27550, 43411, 68403, 107783, 169834, 267606, 421666, 664419, 1046925, 1649640, 2599335, 4095768, 6453698, 10169086, 16023420, 25248087, 39783383
OFFSET
0,4
FORMULA
G.f.: 1 / (1 - Sum_{k>=2} x^A001045(k)).
MATHEMATICA
nmax = 40; CoefficientList[Series[1/(1 - Sum[x^((2^k - (-1)^k)/3), {k, 2, 20}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 02 2022
STATUS
approved