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

A371743 a(n) = Sum_{k=0..floor(n/2)} binomial(4*n-k,n-2*k).

Original entry on oeis.org

1, 4, 29, 231, 1926, 16491, 143683, 1267395, 11282393, 101151544, 912011633, 8260998772, 75115815749, 685232639419, 6268299350776, 57478389714473, 528167137069958, 4862304525663579, 44836026545219765, 414048025058547788, 3828677665694353049
Offset: 0

Views

Author

Seiichi Manyama, Apr 05 2024

Keywords

Crossrefs

Cf. A108081, A371742, A371744.

Programs

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

Formula

a(n) = [x^n] 1/((1-x-x^2) * (1-x)^(3*n)).
a(n) ~ 2^(8*n + 5/2) / (11 * sqrt(Pi*n) * 3^(3*n - 1/2)). - Vaclav Kotesovec, Apr 05 2024

A371787 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(5*n-k,n-2*k).

Original entry on oeis.org

1, 5, 44, 441, 4675, 51129, 570401, 6451688, 73715212, 848793726, 9833394285, 114487194485, 1338411363535, 15700659542105, 184722993467063, 2178831068873601, 25756348168285379, 305061478075705411, 3619402085862708614, 43008294559624639777
Offset: 0

Views

Author

Seiichi Manyama, Apr 06 2024

Keywords

Crossrefs

Cf. A024718, A371785, A371786.
Cf. A371744.

Programs

  • PARI
    a(n) = sum(k=0, n\2, (-1)^k*binomial(5*n-k, n-2*k));

Formula

a(n) = [x^n] 1/((1-x+x^2) * (1-x)^(4*n)).
It appears that a(n) = Sum_{k = 0..n} binomial(3*n+2*k-1, k). - Peter Bala, Jun 04 2024
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.