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.

A322798 Number of compositions (ordered partitions) of n into hexagonal numbers (A000384).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 12, 16, 22, 29, 37, 47, 60, 77, 101, 133, 174, 226, 292, 376, 486, 632, 823, 1072, 1394, 1808, 2342, 3036, 3939, 5116, 6648, 8636, 11211, 14548, 18875, 24493, 31795, 41283, 53604, 69594, 90338, 117251, 152184, 197540
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 26 2018

Keywords

Links

Crossrefs

Cf. A000384, A006456, A023361, A181324, A278949, A279279, A322799, A322800.

Programs

  • Maple
    h:= proc(n) option remember; `if`(n<1, 0, (t->
      `if`(t*(2*t-1)>n, t-1, t))(1+h(n-1)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-i*(2*i-1)), i=1..h(n)))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Dec 28 2018
  • Mathematica
    nmax = 50; CoefficientList[Series[1/(1 - Sum[x^(k (2 k - 1)), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

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

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))).

A322803 Number of compositions (ordered partitions) of n into centered heptagonal numbers (A069099).

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, 45, 55, 67, 82, 101, 125, 155, 192, 239, 297, 368, 455, 562, 694, 857, 1058, 1308, 1619, 2005, 2483, 3074, 3805, 4708, 5822, 7198, 8900, 11007, 13616, 16846, 20845, 25795, 31918, 39489
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 26 2018

Keywords

Links

Crossrefs

Cf. A069099, A280863, A282502, A282504, A322799, A322801, A322802.

Programs

  • Maple
    h:= proc(n) option remember; `if`(n<1, 0, (t->
      `if`((7*(t-1)*t+2)/2>n, t-1, t))(1+h(n-1)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-(7*(i-1)*i+2)/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^(7 k (k + 1)/2 + 1), {k, 0, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=0} x^(7*k*(k+1)/2+1)).

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)).

A332015 Number of compositions (ordered partitions) of n into distinct heptagonal numbers.

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Feb 04 2020

Keywords

Examples

			a(26) = 6 because we have [18, 7, 1], [18, 1, 7], [7, 18, 1], [7, 1, 18], [1, 18, 7] and [1, 7, 18].

Links

Crossrefs

Cf. A000566, A279012, A279280, A322799, A331843, A331844, A332007, A332014, A332016.

A363149 Expansion of 1 / Sum_{k>=0} x^(k*(5*k - 3)/2).

Original entry on oeis.org

1, -1, 1, -1, 1, -1, 1, -2, 3, -4, 5, -6, 7, -8, 10, -13, 17, -22, 27, -33, 40, -49, 61, -77, 98, -123, 153, -189, 233, -288, 358, -448, 561, -701, 872, -1082, 1342, -1666, 2073, -2584, 3223, -4016, 4997, -6212, 7720, -9598, 11942, -14869, 18517, -23053, 28687
Offset: 0

Views

Author

Ilya Gutkovskiy, May 25 2023

Keywords

Crossrefs

Cf. A000566, A106507, A308806, A317665, A322799, A361979, A363275.

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[1/Sum[x^(k (5 k - 3)/2), {k, 0, nmax}], {x, 0, nmax}], x]
Showing 1-6 of 6 results.

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