A357452 -id:A357452 - cp's OEIS frontend

A357453 Number of compositions (ordered partitions) of n into tetranacci numbers 1,2,4,8,15,29, ... (A000078).

1, 1, 2, 3, 6, 10, 18, 31, 56, 98, 174, 306, 542, 956, 1690, 2984, 5273, 9313, 16453, 29062, 51340, 90689, 160203, 282994, 499908, 883078, 1559948, 2755624, 4867776, 8598858, 15189770, 26832521, 47399291, 83730207, 147908288, 261277998, 461544073

Offset: 0

Ilya Gutkovskiy, Sep 29 2022

nonn

Cf. A000078, A076739, A287656, A357451, A357452, A357455.

A000078[0] = A000078[1] = A000078[2] = 0; A000078[3] = 1; A000078[n_] := A000078[n] = A000078[n - 1] + A000078[n - 2] + A000078[n - 3] + A000078[n - 4]; nmax = 36; CoefficientList[Series[1/(1 - Sum[x^A000078[k], {k, 4, 20}]), {x, 0, nmax}], x]

G.f.: 1 / (1 - Sum_{k>=4} x^A000078(k)).

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Sep 29 2022

nonn

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

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]

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

cp's OEIS Frontend

A357453 Number of compositions (ordered partitions) of n into tetranacci numbers 1,2,4,8,15,29, ... (A000078).

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