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.

A371742 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-k,n-2*k).

Original entry on oeis.org

1, 3, 16, 92, 551, 3380, 21065, 132771, 843944, 5399802, 34731776, 224361283, 1454557294, 9458829681, 61670895633, 403003997300, 2638776935215, 17308508054848, 113709379928689, 748069400432262, 4927608724973776, 32495826854732633, 214521754579553129
Offset: 0

Views

Author

Seiichi Manyama, Apr 05 2024

Keywords

Crossrefs

Cf. A108081, A371743, A371744.
Cf. A066380, A371754.
Cf. A183160.

Programs

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

Formula

a(n) = [x^n] 1/((1-x-x^2) * (1-x)^(2*n)).
a(n) ~ 3^(3*n + 3/2) / (5 * sqrt(Pi*n) * 2^(2*n)). - Vaclav Kotesovec, Apr 05 2024

A371744 a(n) = Sum_{k=0..floor(n/2)} binomial(5*n-k,n-2*k).

Original entry on oeis.org

1, 5, 46, 469, 5017, 55177, 617905, 7008264, 80241790, 925457822, 10735707149, 125128265025, 1464140655619, 17188834766497, 202366206841241, 2388313959181973, 28246993739096305, 334711010978735163, 3972765235517468758, 47224110710958716845
Offset: 0

Views

Author

Seiichi Manyama, Apr 05 2024

Keywords

Crossrefs

Cf. A108081, A371742, A371743.

Programs

  • PARI
    a(n) = sum(k=0, n\2, binomial(5*n-k, n-2*k));

Formula

a(n) = [x^n] 1/((1-x-x^2) * (1-x)^(4*n)).
a(n) ~ 5^(5*n + 3/2) / (19 * sqrt(Pi*n) * 2^(8*n - 1/2)). - Vaclav Kotesovec, Apr 05 2024

A371786 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(4*n-k,n-2*k).

Original entry on oeis.org

1, 4, 27, 209, 1716, 14553, 125971, 1105885, 9809019, 87691592, 788832045, 7131655908, 64743390321, 589808771881, 5389066722654, 49365637128655, 453212161425716, 4168951499299185, 38415242186255419, 354527945536409116, 3276414018301664025
Offset: 0

Views

Author

Seiichi Manyama, Apr 06 2024

Keywords

Crossrefs

Cf. A024718, A371785, A371787.
Cf. A371743.

Programs

  • PARI
    a(n) = sum(k=0, n\2, (-1)^k*binomial(4*n-k, n-2*k));

Formula

a(n) = [x^n] 1/((1-x+x^2) * (1-x)^(3*n)).
Showing 1-3 of 3 results.

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

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