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 1-3 of 3 results.

A369437 a(n) = [x^n] Product_{k=1..n} (x^(k^3) + 1 + 1/x^(k^3)).

Original entry on oeis.org

1, 1, 0, 0, 0, 0, 0, 4, 6, 15, 24, 40, 69, 138, 396, 1028, 3062, 8269, 21680, 50955, 115457, 262239, 631393, 1666438, 4558051, 12913587, 35530351, 95825467, 246943968, 628040166, 1607703060, 4228528070, 11485131123, 31616483271, 88141192570, 243487667830
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 23 2024

Keywords

Links

Crossrefs

Cf. A000578, A316706, A348892, A369345.

Programs

  • Maple
    b:= proc(n, i) option remember; `if`(n>(i*(i+1)/2)^2, 0,
     `if`(i=0, 1, b(n, i-1)+b(n+i^3, i-1)+b(abs(n-i^3), i-1)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..35);  # Alois P. Heinz, Jan 23 2024
  • Mathematica
    Table[Coefficient[Product[(x^(k^3) + 1 + 1/x^(k^3)), {k, 1, n}], x, n], {n, 0, 34}]

A369735 Number of solutions to 1^3*k_1 + 2^3*k_2 + ... + n^3*k_n = 1, where k_i are from {-1,0,1}, i=1..n.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 3, 4, 6, 15, 28, 56, 125, 287, 646, 1540, 3625, 8484, 21167, 51458, 126342, 323126, 811538, 2052501, 5339265, 13751212, 35589866, 94032931, 246791641, 650227636, 1739032299, 4630165425, 12373805281, 33429284691, 90073865814, 243460560324
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 30 2024

Keywords

Crossrefs

Cf. A007576, A063866, A369345, A369437, A369628, A369734.

Programs

  • Maple
    b:= proc(n, i) option remember; `if`(n>(i*(i+1)/2)^2, 0,
     `if`(i=0, 1, b(n, i-1)+b(n+i^3, i-1)+b(abs(n-i^3), i-1)))
    end:
a:= n-> b(1, n):
seq(a(n), n=0..35);  # Alois P. Heinz, Jan 30 2024
  • Mathematica
    Table[Coefficient[Product[(x^(k^3) + 1 + 1/x^(k^3)), {k, 1, n}], x, 1], {n, 0, 33}]

Formula

a(n) = [x^1] Product_{k=1..n} (x^(k^3) + 1 + 1/x^(k^3)).

A369438 a(n) = [x^(n^3)] Product_{k=1..n} (x^(k^3) + 1 + 1/x^(k^3)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 3, 4, 11, 24, 46, 106, 238, 537, 1318, 3007, 7027, 18199, 43202, 105900, 279860, 688474, 1741235, 4641670, 11790546, 30529486, 82306963, 213852619, 563866091, 1531711961, 4047719392, 10835966180, 29624064007, 79423421277, 215083283638
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 23 2024

Keywords

Crossrefs

Cf. A000578, A316706, A368845, A369345.

Programs

  • Maple
    b:= proc(n, i) option remember; `if`(n>(i*(i+1)/2)^2, 0,
     `if`(i=0, 1, b(n, i-1)+b(n+i^3, i-1)+b(abs(n-i^3), i-1)))
    end:
a:= n-> b(n^3, n):
seq(a(n), n=0..35);  # Alois P. Heinz, Jan 23 2024
  • Mathematica
    Table[Coefficient[Product[(x^(k^3) + 1 + 1/x^(k^3)), {k, 1, n}], x, n^3], {n, 0, 34}]
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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