A357454 -id:A357454

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A357455

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

+10
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

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..37.

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

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

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 29 2022

STATUS

approved

A357452

Number of partitions of n into tetranacci numbers 1,2,4,8,15,29, ... (A000078).

+10
2

1, 1, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 20, 20, 26, 27, 36, 37, 46, 48, 60, 62, 74, 78, 94, 98, 114, 120, 140, 147, 168, 178, 204, 215, 242, 256, 288, 304, 338, 358, 398, 420, 462, 488, 537, 567, 619, 654, 714, 753, 816, 860, 932, 982, 1058, 1114