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.

A375158 Expansion of Sum_{k in Z} x^(2*k) / (1 - x^(7*k+2)).

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 01 2024

Keywords

Crossrefs

Cf. A375107, A375148, A375159.
Cf. A374900, A375108.

Programs

  • PARI
    my(N=110, x='x+O('x^N)); Vec(sum(k=-N, N, x^(2*k)/(1-x^(7*k+2))))
  • PARI
    my(N=110, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(7*k))^2*(1-x^(7*k-3))*(1-x^(7*k-4))/((1-x^(7*k-2))*(1-x^(7*k-5)))^2))

Formula

G.f.: Product_{k>0} (1-x^(7*k))^2 * (1-x^(7*k-3)) * (1-x^(7*k-4)) / ((1-x^(7*k-2)) * (1-x^(7*k-5)))^2.

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.

A373419 Expansion of B(x)^2, where B(x) is the g.f. of A108482.

Original entry on oeis.org

1, 2, 3, 2, -1, -4, -4, 0, 7, 10, 5, -8, -20, -18, 1, 28, 40, 20, -25, -64, -59, 2, 81, 114, 55, -74, -178, -158, 9, 220, 301, 144, -183, -444, -390, 16, 518, 706, 330, -430, -1019, -884, 46, 1170, 1575, 738, -931, -2202, -1902, 84, 2460, 3292, 1523, -1938, -4541, -3888, 186, 4994, 6646, 3066, -3842
Offset: 0

Views

Author

Seiichi Manyama, Aug 03 2024

Keywords

Crossrefs

Cf. A108482, A375148, A375159.

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-1))*(1-x^(7*k-6))))^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 A375159.
Showing 1-3 of 3 results.

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

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