A357454 -id:A357454 - cp's OEIS frontend

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

Ilya Gutkovskiy, Sep 29 2022

nonn

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

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]

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

A357452 Number of partitions of n into tetranacci numbers 1,2,4,8,15,29, ... (A000078).

Original entry on oeis.org

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

Offset: 0

Ilya Gutkovskiy, Sep 29 2022

nonn

Cf. A000078, A003107, A240844, A287656, A357453, A357454.

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 = 55; CoefficientList[Series[Product[1/(1 - x^A000078[k]), {k, 4, 20}], {x, 0, nmax}], x]

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

cp's OEIS Frontend

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

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula