cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A322853 Number of compositions (ordered partitions) of n into pentagonal pyramidal numbers (A002411).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 12, 16, 21, 27, 34, 44, 57, 74, 96, 124, 159, 205, 265, 343, 444, 574, 740, 954, 1231, 1590, 2055, 2656, 3430, 4428, 5716, 7380, 9531, 12312, 15902, 20536, 26518, 34242, 44218, 57106, 73751, 95245, 122999, 158837, 205117
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 29 2018

Keywords

Links

Crossrefs

Cf. A002411, A181324, A279221, A282582, A322340, A322801, A322854, A322855, A322856.

Programs

  • Mathematica
    nmax = 51; CoefficientList[Series[1/(1 - Sum[x^(k^2 (k + 1)/2), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k^2*(k+1)/2)).

A322854 Number of compositions (ordered partitions) of n into hexagonal pyramidal numbers (A002412).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 17, 22, 28, 35, 43, 53, 67, 85, 108, 137, 173, 217, 271, 340, 428, 540, 682, 861, 1085, 1364, 1714, 2155, 2712, 3416, 4305, 5425, 6832, 8599, 10821, 13618, 17142, 21584, 27182, 34231, 43102, 54264, 68311, 85994
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 29 2018

Keywords

Links

Crossrefs

Cf. A002412, A279222, A282582, A322340, A322798, A322802, A322853, A322855, A322856.

Programs

  • Mathematica
    nmax = 53; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (4 k - 1)/6), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(4*k-1)/6)).

A322855 Number of compositions (ordered partitions) of n into heptagonal pyramidal numbers (A002413).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 18, 23, 29, 36, 44, 53, 64, 78, 97, 121, 151, 188, 233, 287, 352, 431, 530, 654, 809, 1002, 1241, 1535, 1895, 2335, 2876, 3544, 4371, 5396, 6666, 8237, 10176, 12564, 15504, 19126, 23594, 29111, 35928
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 29 2018

Keywords

Links

Crossrefs

Cf. A002413, A279223, A282582, A322340, A322799, A322803, A322853, A322854, A322856.

Programs

  • Mathematica
    nmax = 54; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (5 k - 2)/6), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(5*k-2)/6)).

A322856 Number of compositions (ordered partitions) of n into octagonal pyramidal numbers (A002414).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 19, 24, 30, 37, 45, 54, 64, 76, 91, 110, 135, 166, 204, 250, 305, 370, 447, 539, 650, 787, 956, 1164, 1419, 1730, 2107, 2562, 3110, 3770, 4569, 5540, 6723, 8166, 9926, 12070, 14677, 17841, 21675
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 29 2018

Keywords

Links

Crossrefs

Cf. A002414, A279224, A280863, A282582, A322340, A322800, A322853, A322854, A322855.

Programs

  • Mathematica
    nmax = 56; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (2 k - 1)/2), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(2*k-1)/2)).

A331984 Number of compositions (ordered partitions) of n into distinct square pyramidal numbers.

Original entry on oeis.org

1, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 6, 24, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 6, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 6, 25
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 03 2020

Keywords

Examples

			a(20) = 6 because we have [14, 5, 1], [14, 1, 5], [5, 14, 1], [5, 1, 14], [1, 14, 5] and [1, 5, 14].

Links

Crossrefs

Cf. A000330, A279220, A298246, A322340, A331844, A331919.
Showing 1-5 of 5 results.

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