A357455 Number of compositions (ordered partitions) of n into pentanacci numbers 1,2,4,8,16,31, ... (A001591).

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

Author

Ilya Gutkovskiy, Sep 29 2022

Keywords

• nonn

Crossrefs

Cf. A001591, A076739, A288120, A357451, A357453, A357454.

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 = 37; CoefficientList[Series[1/(1 - Sum[x^A001591[k], {k, 5, 20}]), {x, 0, nmax}], x]

Formula

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