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A357455
Number of compositions (ordered partitions) of n into pentanacci numbers 1,2,4,8,16,31, ... (A001591).
3
1, 1, 2, 3, 6, 10, 18, 31, 56, 98, 174, 306, 542, 956, 1690, 2983, 5272, 9310, 16448, 29050, 51318, 90644, 160118, 282826, 499590, 882468, 1558798, 2753448, 4863696, 8591212, 15175514, 26805984, 47350057, 83639033, 147739853, 260967374, 460972308, 814260589
OFFSET
0,3
FORMULA
G.f.: 1 / (1 - Sum_{k>=5} x^A001591(k)).
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 = 37; CoefficientList[Series[1/(1 - Sum[x^A001591[k], {k, 5, 20}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 29 2022
STATUS
approved