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 1-6 of 6 results.

A322799 Number of compositions (ordered partitions) of n into heptagonal numbers (A000566).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 17, 22, 29, 37, 46, 57, 71, 89, 112, 143, 183, 233, 295, 372, 468, 588, 741, 937, 1188, 1506, 1908, 2414, 3049, 3848, 4857, 6136, 7757, 9812, 12414, 15702, 19852, 25089, 31703, 40061, 50631, 64004, 80923, 102318
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 26 2018

Keywords

Links

Crossrefs

Cf. A000566, A006456, A023361, A181324, A279012, A279280, A322798, A322800.

Programs

  • Maple
    h:= proc(n) option remember; `if`(n<1, 0, (t->
      `if`(t*(5*t-3)/2>n, t-1, t))(1+h(n-1)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-i*(5*i-3)/2), i=1..h(n)))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Dec 28 2018
  • Mathematica
    nmax = 53; CoefficientList[Series[1/(1 - Sum[x^(k (5 k - 3)/2), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k*(5*k-3)/2)).

A322800 Number of compositions (ordered partitions) of n into octagonal numbers (A000567).

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, 37, 46, 56, 68, 83, 102, 126, 156, 195, 244, 304, 377, 466, 575, 709, 874, 1080, 1338, 1660, 2061, 2557, 3170, 3926, 4857, 6006, 7428, 9191, 11380, 14096, 17465, 21640, 26807, 33197, 41099
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 26 2018

Keywords

Links

Crossrefs

Cf. A000567, A006456, A023361, A181324, A279041, A279281, A322798, A322799.

Programs

  • Maple
    h:= proc(n) option remember; `if`(n<1, 0, (t->
      `if`(t*(3*t-2)>n, t-1, t))(1+h(n-1)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-i*(3*i-2)), i=1..h(n)))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Dec 28 2018
  • Mathematica
    nmax = 54; CoefficientList[Series[1/(1 - Sum[x^(k (3 k - 2)), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k*(3*k-2))).

A322802 Number of compositions (ordered partitions) of n into centered hexagonal numbers (A003215).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 17, 22, 28, 36, 45, 56, 70, 88, 111, 140, 178, 226, 286, 361, 455, 573, 721, 909, 1148, 1451, 1834, 2318, 2928, 3695, 4661, 5880, 7420, 9366, 11826, 14935, 18860, 23812, 30059, 37941, 47888, 60445, 76302, 96327
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 26 2018

Keywords

Links

Crossrefs

Cf. A003215, A280863, A280953, A281084, A282502, A282504, A322798, A322801, A322803.

Programs

  • Maple
    h:= proc(n) option remember; `if`(n<0, 0, (t->
      `if`(3*t*(t+1)+1>n, t-1, t))(1+h(n-1)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-(3*i*(i+1)+1)), i=0..h(n)))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Dec 28 2018
  • Mathematica
    nmax = 53; CoefficientList[Series[1/(1 - Sum[x^(3 k (k + 1) + 1), {k, 0, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=0} x^(3*k*(k+1)+1)).

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)).

A332014 Number of compositions (ordered partitions) of n into distinct hexagonal numbers.

Original entry on oeis.org

1, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 2, 6, 1, 2, 0, 0, 6, 24, 2, 6, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 7, 26, 0, 0, 0, 0, 2, 8, 6, 0, 0, 0, 0, 6, 24
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 04 2020

Keywords

Examples

			a(22) = 6 because we have [15, 6, 1], [15, 1, 6], [6, 15, 1], [6, 1, 15], [1, 15, 6] and [1, 6, 15].

Links

Crossrefs

Cf. A000384, A278949, A279279, A322798, A331843, A331844, A332007, A332015, A332016.

A361979 Expansion of 1 / Sum_{k>=0} x^(k*(2*k - 1)).

Original entry on oeis.org

1, -1, 1, -1, 1, -1, 0, 1, -2, 3, -4, 5, -5, 4, -2, -2, 7, -13, 19, -24, 27, -25, 17, -2, -20, 48, -80, 110, -132, 137, -116, 62, 30, -158, 314, -479, 622, -704, 680, -507, 150, 405, -1135, 1973, -2797, 3432, -3662, 3250, -1983, -280, 3540, -7592, 11977, -15953
Offset: 0

Views

Author

Ilya Gutkovskiy, May 25 2023

Keywords

Crossrefs

Cf. A000384, A006950, A106507, A308806, A317665, A322798, A363149, A363275.

Programs

  • Mathematica
    nmax = 53; CoefficientList[Series[1/Sum[x^(k (2 k - 1)), {k, 0, nmax}], {x, 0, nmax}], x]
Showing 1-6 of 6 results.

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