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.

A375106 Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+3)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 0, 2, 1, 0, 2, 1, 1, 1, 1, 1, 2, 0, 1, 0, 1, 1, 3, 1, 1, 0, 1, 2, 1, 1, 1, 1, 0, 0, 2, 1, 1, 2, 1, 1, 2, 0, 1, 1, 1, 0, 2, 2, 1, 0, 0, 1, 3, 1, 1, 0, 2, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 3, 1, 1, 2, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 0
Offset: 0

Views

Author

Seiichi Manyama, Jul 30 2024

Keywords

Links

Crossrefs

Cf. A374900, A375148, A375149, A375150.
Cf. A375107, A375108.

Programs

  • PARI
    my(N=100, x='x+O('x^N)); Vec(sum(k=-N, N, x^k/(1-x^(7*k+3))))
  • PARI
    my(N=100, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^2/((1-x^(7*k-1))*(1-x^(7*k-6)))))

Formula

G.f.: Product_{k>0} (1-x^(7*k))^2 / ((1-x^(7*k-1)) * (1-x^(7*k-6))).
G.f.: Sum_{k in Z} x^(3*k) / (1 - x^(7*k+1)).

A375148 Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+2)).

Original entry on oeis.org

1, 1, 2, 1, 1, 1, 2, 1, 2, 0, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 0, 1, 1, 1, 3, 1, 2, 0, 2, 1, 2, 1, 1, 0, 2, 2, 2, 0, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 0, 2, 2, 1, 1, 0, 2, 0, 2, 1, 2, 1, 4, 1, 2, 0, 0, 1, 3, 1, 0, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1, 2, 0, 1, 0, 3, 2, 1, 1, 0, 2, 2, 1, 4, 0, 0
Offset: 0

Views

Author

Seiichi Manyama, Aug 01 2024

Keywords

Crossrefs

Cf. A374900, A375106, A375149, A375150.
Cf. A033687, A340453.

Programs

  • PARI
    my(N=110, x='x+O('x^N)); Vec(sum(k=-N, N, x^k/(1-x^(7*k+2))))
  • PARI
    my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^3*((1-x^(7*k-3))*(1-x^(7*k-4)))^2/(1-x^k)))

Formula

G.f.: Product_{k>0} (1-x^(7*k))^3 * ((1-x^(7*k-3)) * (1-x^(7*k-4)))^2 / (1-x^k).
G.f.: Sum_{k in Z} x^(2*k) / (1 - x^(7*k+1)).

A375150 Expansion of Sum_{k in Z} x^k / (1 - x^(7*k+5)).

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 1, -1, 1, 0, 2, 0, 1, 0, 1, 1, 0, 0, 1, -1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 2, -1, 1, 0, 0, 1, 1, 1, 1, 0, 3, 0, 0, -2, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 2, -1, 1, 0, 1, 0, 1, -1, 0, 1, 2, 0, 1, 0, 1, 1, 1, 0, 2, -2, 2, 0, 1, 0, 1, 2, 1, 0, -1, 0, 2, -1, 1, 0, 0, 1, 1, 0, 1, 0, 3
Offset: 0

Views

Author

Seiichi Manyama, Aug 01 2024

Keywords

Crossrefs

Cf. A374900, A375106, A375148, A375149.
Cf. A375107.

Programs

  • PARI
    my(N=110, x='x+O('x^N)); Vec(sum(k=-N, N, x^k/(1-x^(7*k+5))))
  • PARI
    my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^2/((1-x^(7*k-2))*(1-x^(7*k-5)))))

Formula

G.f.: Product_{k>0} (1-x^(7*k))^2 / ((1-x^(7*k-2)) * (1-x^(7*k-5))).
G.f.: Sum_{k in Z} x^(5*k) / (1 - x^(7*k+1)).

A375159 Expansion of Sum_{k in Z} x^(4*k) / (1 - x^(7*k+2)).

Original entry on oeis.org

1, -1, 1, 0, 1, 0, 0, -1, 2, 0, 0, -1, 2, 0, 1, 0, -1, 0, 1, -1, 2, -1, 1, 0, 3, -1, -1, 0, 0, 0, 1, -1, 2, 0, 0, 1, 0, -1, 1, 0, 2, -1, 1, -1, 2, -1, -1, 0, 2, 0, 1, -1, 0, 0, 1, -1, 1, 1, 2, 0, 2, -2, 0, 0, -1, 0, -1, 0, 3, 0, 0, -1, 3, -1, 1, 0, 0, 0, 1, -1, 2, 0, 0, -1, 2, 0, -1, 0, 0, 0, 2, -2, 2, 0, 2, 0, -1, -1, 1, 0, 0
Offset: 0

Views

Author

Seiichi Manyama, Aug 01 2024

Keywords

Crossrefs

Cf. A375107, A375148, A375158.
Cf. A375149.

Programs

  • PARI
    my(N=110, x='x+O('x^N)); Vec(sum(k=-N, N, x^(4*k)/(1-x^(7*k+2))))
  • PARI
    my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^3*((1-x^(7*k-1))*(1-x^(7*k-6)))^2/(1-x^k)))

Formula

G.f.: Product_{k>0} (1-x^(7*k))^3 * ((1-x^(7*k-1)) * (1-x^(7*k-6)))^2 / (1-x^k).
G.f.: Sum_{k in Z} x^(2*k) / (1 - x^(7*k+4)).

A373121 Expansion of B(x)^2, where B(x) is the g.f. of A230322.

Original entry on oeis.org

1, 0, 2, -2, 1, -2, 1, 2, -2, 4, -6, 4, -4, 0, 5, -6, 13, -14, 9, -10, 1, 12, -16, 26, -32, 24, -19, 2, 22, -34, 57, -64, 48, -40, 4, 44, -70, 108, -124, 98, -73, 6, 79, -132, 205, -228, 181, -134, 13, 142, -245, 360, -404, 330, -230, 18, 241, -428, 630, -694, 567, -394, 35, 410, -735, 1054
Offset: 0

Views

Author

Seiichi Manyama, Aug 03 2024

Keywords

Crossrefs

Cf. A230322, A375148, A375149.

Programs

  • PARI
    my(N=70, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k-3))*(1-x^(7*k-4))/((1-x^(7*k-2))*(1-x^(7*k-5))))^2)

Formula

G.f.: C(x) / D(x), where C(x) is the g.f. of A375148 and D(x) is the g.f. of A375149.

A373122 Expansion of B(x)^2, where B(x) is the g.f. of A108483.

Original entry on oeis.org

1, 2, 1, 0, 0, -2, -2, 2, 4, 2, -1, -4, -6, -4, 5, 12, 7, -2, -10, -16, -9, 12, 25, 16, -5, -24, -34, -18, 26, 54, 36, -8, -50, -70, -35, 48, 102, 70, -16, -100, -134, -62, 93, 194, 137, -26, -186, -246, -114, 164, 341, 244, -47, -338, -434, -192, 289, 598, 433, -76, -583, -748, -325, 486, 1001
Offset: 0

Views

Author

Seiichi Manyama, Aug 03 2024

Keywords

Crossrefs

Cf. A108483, A375149, A375159.

Programs

  • PARI
    my(N=70, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k-2))*(1-x^(7*k-5))/((1-x^(7*k-1))*(1-x^(7*k-6))))^2)

Formula

G.f.: C(x) / D(x), where C(x) is the g.f. of A375149 and D(x) is the g.f. of A375159.
Showing 1-6 of 6 results.

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

Content is available under The OEIS End-User License Agreement.