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 1-2 of 2 results.

A360314 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-1-2*k,n-3*k) * binomial(2*k,k).

Original entry on oeis.org

1, 0, 0, -2, -2, -2, 4, 10, 16, 2, -32, -86, -90, 26, 332, 646, 534, -690, -3040, -4934, -2270, 9066, 27260, 35198, 532, -101946, -232752, -230730, 158986, 1039078, 1899364, 1265370, -2714160, -9926158, -14625008, -4036358, 34062386, 89744810, 104123084
Offset: 0

Views

Author

Seiichi Manyama, Feb 03 2023

Keywords

Crossrefs

Cf. A360313, A360315.
Cf. A360294, A360309.

Programs

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

Formula

G.f.: 1 / sqrt(1+4*x^3/(1-x)).
n*a(n) = 2*(n-1)*a(n-1) - (n-2)*a(n-2) - 2*(2*n-3)*a(n-3) + 2*(2*n-6)*a(n-4).

A360315 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-1-3*k,n-4*k) * binomial(2*k,k).

Original entry on oeis.org

1, 0, 0, 0, -2, -2, -2, -2, 4, 10, 16, 22, 8, -26, -80, -154, -178, -82, 204, 750, 1374, 1642, 868, -1886, -6886, -12802, -15784, -8538, 17166, 64554, 122476, 152602, 86056, -157642, -616456, -1183666, -1493402, -878250, 1468080
Offset: 0

Views

Author

Seiichi Manyama, Feb 03 2023

Keywords

Crossrefs

Cf. A360313, A360314.
Cf. A360295, A360310.

Programs

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

Formula

G.f.: 1 / sqrt(1+4*x^4/(1-x)).
n*a(n) = 2*(n-1)*a(n-1) - (n-2)*a(n-2) - 2*(2*n-4)*a(n-4) + 2*(2*n-7)*a(n-5).
Showing 1-2 of 2 results.

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

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