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 1-4 of 4 results.

A373067 Number of partitions of n such that (smallest part) >= 2*(number of parts).

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 8, 10, 11, 13, 14, 17, 18, 21, 23, 26, 28, 32, 34, 39, 42, 47, 51, 58, 62, 70, 76, 85, 92, 103, 111, 124, 134, 148, 160, 177, 190, 210, 226, 248, 267, 293, 315, 345, 371, 405, 436, 476, 511, 557, 599, 651, 700, 760, 816
Offset: 0

Views

Author

Seiichi Manyama, May 22 2024

Keywords

Crossrefs

Cf. A003114, A373068, A373069, A373070.
Cf. A069910, A350893, A373073.

Programs

  • PARI
    my(N=70, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k^2)/prod(j=1, k, 1-x^j)))

Formula

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

A373069 Number of partitions of n such that (smallest part) >= 4*(number of parts).

Original entry on oeis.org

1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 13, 13, 15, 16, 18, 19, 22, 23, 26, 28, 31, 33, 37, 39, 43, 46, 50, 53, 58, 61, 66, 70, 75, 79, 85, 89, 95, 100, 107, 112, 120, 126, 135, 142, 152, 160, 172, 181, 194, 205, 220, 232, 249, 263
Offset: 0

Views

Author

Seiichi Manyama, May 22 2024

Keywords

Crossrefs

Cf. A003114, A373067, A373068, A373070.
Cf. A350898, A373075.

Programs

  • PARI
    my(N=80, x='x+O('x^N)); Vec(sum(k=0, N, x^(4*k^2)/prod(j=1, k, 1-x^j)))

Formula

G.f.: Sum_{k>=0} x^(4*k^2)/Product_{j=1..k} (1-x^j).

A373070 Number of partitions of n such that (smallest part) >= 5*(number of parts).

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 15, 16, 17, 19, 20, 22, 24, 26, 28, 31, 33, 36, 39, 42, 45, 49, 52, 56, 60, 64, 68, 73, 77, 82, 87, 92, 97, 103, 108, 114, 120, 126, 132, 139, 145, 153, 160, 168, 176, 186, 194
Offset: 0

Views

Author

Seiichi Manyama, May 22 2024

Keywords

Crossrefs

Cf. A003114, A373067, A373068, A373069.
Cf. A350899, A373076.

Programs

  • PARI
    my(N=90, x='x+O('x^N)); Vec(sum(k=0, N, x^(5*k^2)/prod(j=1, k, 1-x^j)))

Formula

G.f.: Sum_{k>=0} x^(5*k^2)/Product_{j=1..k} (1-x^j).

A373074 Number of partitions of n such that (smallest part) > 3*(number of parts).

Original entry on oeis.org

1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 11, 11, 13, 14, 16, 17, 20, 21, 24, 26, 29, 31, 35, 37, 41, 44, 48, 51, 56, 59, 64, 68, 74, 78, 85, 90, 98, 104, 113, 120, 131, 139, 151, 161, 175, 186, 202, 215, 233, 248, 268, 285, 308, 327, 352, 374, 402, 426, 457
Offset: 0

Views

Author

Seiichi Manyama, May 22 2024

Keywords

Crossrefs

Cf. A003106, A373073, A373075, A373076.
Cf. A350894, A373068.

Programs

Formula

G.f.: Sum_{k>=0} x^(3*k^2+k)/Product_{j=1..k} (1-x^j).
Showing 1-4 of 4 results.

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

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