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.

A364594 G.f. satisfies A(x) = 1/(1-x) + x^2*(1-x)*A(x)^4.

Original entry on oeis.org

1, 1, 2, 4, 11, 31, 98, 316, 1065, 3649, 12775, 45299, 162713, 590097, 2159015, 7957003, 29517141, 110116277, 412879256, 1555048142, 5880591163, 22319380999, 84992915958, 324634976440, 1243396473153, 4774504667881, 18376620653851, 70883537152927
Offset: 0

Views

Author

Seiichi Manyama, Jul 29 2023

Keywords

Crossrefs

Cf. A110199, A364593.
Cf. A364592, A364596.

Programs

  • PARI
    a(n) = sum(k=0, n\2, binomial(n, 2*k)*binomial(4*k, k)/(3*k+1));

Formula

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

A166446 Period 12: repeat [1,1,1,1,0,0,-1,-1,-1,-1,0,0].

Original entry on oeis.org

1, 1, 1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0
Offset: 0

Views

Author

Paul Barry, Oct 13 2009

Keywords

Comments

a(n+2) is the Hankel transform of A110199. - Paul Barry, Jun 23 2010

Links

Crossrefs

Cf. A010892 (bisection).

Programs

  • Magma
    &cat [[1,1,1,1,0,0,-1,-1,-1,-1,0,0]^^10]; // Vincenzo Librandi, May 15 2016
  • Mathematica
    LinearRecurrence[{0,1,0,-1}, {1,1,1,1}, 50] (* G. C. Greubel, May 14 2016 *)

Formula

G.f.: (1+x)/(1-x^2+x^4).
a(n) = a(n-2)-a(n-4). - Wesley Ivan Hurt, May 09 2021

Extensions

Incorrect comment removed - R. J. Mathar, Oct 02 2012

A364593 G.f. satisfies A(x) = 1/(1-x) + x^2*(1-x)*A(x)^3.

Original entry on oeis.org

1, 1, 2, 3, 7, 14, 36, 85, 228, 587, 1612, 4354, 12166, 33832, 95876, 271803, 779287, 2239584, 6483386, 18823945, 54932299, 160771540, 472322632, 1391323310, 4110685812, 12173949214, 36141795088, 107521223008, 320531857144, 957289637952, 2864055208772
Offset: 0

Views

Author

Seiichi Manyama, Jul 29 2023

Keywords

Crossrefs

Cf. A110199, A364594.

Programs

  • PARI
    a(n) = sum(k=0, n\2, binomial(n-k, k)*binomial(3*k, k)/(2*k+1));

Formula

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

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

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