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.

A375255 Expansion of 1/(1 - 2*x + 3*x^2 + 2*x^3 + x^4).

Original entry on oeis.org

1, 2, 1, -6, -20, -26, 19, 162, 339, 180, -1000, -3380, -4459, 3042, 27221, 57614, 31940, -166446, -571161, -764478, 485479, 4573160, 9790000, 5654040, -27693719, -96502718, -131022359, 77196834, 768159900, 1663276734, 998702459, -4605941918, -16302704581
Offset: 0

Views

Author

Seiichi Manyama, Aug 09 2024

Keywords

Links

Crossrefs

Cf. A182890, A375273.
Cf. A375021, A375275.

Programs

  • PARI
    my(N=40, x='x+O('x^N)); Vec(1/(1-2*x+3*x^2+2*x^3+x^4))
  • PARI
    a(n) = sum(k=0, n\2, (-1)^k*binomial(2*n-2*k+2, 2*k+1))/2;

Formula

a(n) = 2*a(n-1) - 3*a(n-2) - 2*a(n-3) - a(n-4).
a(n) = (1/2) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n-2*k+2,2*k+1).

A375292 Expansion of 1/sqrt((1 - x + x^3)^2 + 4*x^4).

Original entry on oeis.org

1, 1, 1, 0, -3, -8, -14, -15, 1, 51, 146, 261, 286, -24, -1029, -2975, -5375, -5930, 591, 22014, 63886, 115947, 128183, -14595, -486466, -1413161, -2569868, -2840890, 361667, 10972167, 31861581, 57980426, 64018181, -8985428, -250991300, -727998021, -1324662165
Offset: 0

Views

Author

Seiichi Manyama, Aug 10 2024

Keywords

Crossrefs

Cf. A375021, A375293.
Cf. A246840.

Programs

  • PARI
    my(N=40, x='x+O('x^N)); Vec(1/sqrt((1-x+x^3)^2+4*x^4))
  • PARI
    a(n) = sum(k=0, n\3, (-1)^k*binomial(n-2*k, k)^2);

Formula

n*a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2) - (2*n-3)*a(n-3) - 2*(n-2)*a(n-4) - (n-3)*a(n-6).
a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-2*k,k)^2.

A375293 Expansion of 1/sqrt((1 - x + x^4)^2 + 4*x^5).

Original entry on oeis.org

1, 1, 1, 1, 0, -3, -8, -15, -23, -26, -12, 37, 144, 326, 564, 753, 633, -281, -2699, -7346, -14333, -21858, -24097, -8635, 45094, 162928, 362513, 620686, 813906, 633510, -495381, -3408175, -8939865, -17141831, -25663802, -27145201, -6079518, 62953931
Offset: 0

Views

Author

Seiichi Manyama, Aug 10 2024

Keywords

Crossrefs

Cf. A375021, A375292.
Cf. A246883.

Programs

  • PARI
    my(N=40, x='x+O('x^N)); Vec(1/sqrt((1-x+x^4)^2+4*x^5))
  • PARI
    a(n) = sum(k=0, n\4, (-1)^k*binomial(n-3*k, k)^2);

Formula

n*a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2) - 2*(n-2)*a(n-4) - (2*n-5)*a(n-5) - (n-4)*a(n-8).
a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-3*k,k)^2.
Showing 1-3 of 3 results.

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

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