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 1-5 of 5 results.

A366556 G.f. A(x) satisfies A(x) = 1 + x + x^4*A(x)^3.

Original entry on oeis.org

1, 1, 0, 0, 1, 3, 3, 1, 3, 15, 30, 30, 27, 87, 252, 420, 475, 747, 2064, 4632, 7203, 9933, 19635, 47025, 92013, 144745, 237510, 498498, 1073817, 1969131, 3267411, 5977881, 12462579, 25035747, 45090936, 79414344, 153115299, 311198457, 600883569, 1090988379, 2012793705
Offset: 0

Views

Author

Seiichi Manyama, Oct 13 2023

Keywords

Crossrefs

Cf. A019497, A366266, A366555.
Cf. A366554, A366558.
Cf. A366592.

Programs

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

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(2*k+1,n-4*k) * binomial(3*k,k)/(2*k+1).
a(n) = A366592(n) + A366592(n-1).

A366554 G.f. A(x) satisfies A(x) = 1 + x + x^4*A(x)^2.

Original entry on oeis.org

1, 1, 0, 0, 1, 2, 1, 0, 2, 6, 6, 2, 5, 20, 30, 20, 19, 70, 140, 140, 112, 266, 630, 840, 762, 1176, 2814, 4620, 5049, 6204, 12936, 24156, 31460, 36894, 63492, 123552, 185471, 228800, 338910, 634920, 1050686, 1411410, 1944800, 3354780, 5820256, 8513804, 11644490
Offset: 0

Views

Author

Seiichi Manyama, Oct 13 2023

Keywords

Crossrefs

Cf. A007477, A025227, A248100.
Cf. A366556, A366558.
Cf. A366589.

Programs

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

Formula

G.f.: A(x) = 2*(1+x) / (1+sqrt(1-4*x^4*(1+x))).
a(n) = Sum_{k=0..floor(n/4)} binomial(k+1,n-4*k) * binomial(2*k,k)/(k+1).
a(n) = A366589(n) + A366589(n-1).

A366595 G.f. A(x) satisfies A(x) = 1 + x^4*(1+x)^3*A(x)^4.

Original entry on oeis.org

1, 0, 0, 0, 1, 3, 3, 1, 4, 24, 60, 80, 82, 222, 796, 1848, 2912, 4452, 11088, 31592, 70467, 125437, 231105, 551775, 1399069, 3068219, 5942937, 12017739, 27966515, 66675777, 145719483, 298344501, 632955999, 1449806573, 3346606719, 7335193353, 15557399668
Offset: 0

Views

Author

Seiichi Manyama, Oct 14 2023

Keywords

Crossrefs

Cf. A366272, A366593, A366594.
Cf. A366589, A366592.
Cf. A366558.

Programs

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

Formula

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

A366557 G.f. A(x) satisfies A(x) = 1 + x + x^3*A(x)^4.

Original entry on oeis.org

1, 1, 0, 1, 4, 6, 8, 29, 84, 162, 360, 1074, 2808, 6444, 16464, 45629, 118244, 297450, 790184, 2138438, 5624136, 14778068, 39767024, 107287122, 286593800, 768920084, 2083170960, 5642886852, 15250029552, 41369986008, 112681853344, 306930498205, 836259756612
Offset: 0

Views

Author

Seiichi Manyama, Oct 13 2023

Keywords

Crossrefs

Cf. A137954, A366267, A366558.
Cf. A366594.

Programs

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

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(3*k+1,n-3*k) * binomial(4*k,k)/(3*k+1).
a(n) = A366594(n) + A366594(n-1).

A366677 G.f. satisfies A(x) = 1 + x^4 + x*A(x)^4.

Original entry on oeis.org

1, 1, 4, 22, 141, 973, 7112, 54040, 422552, 3377770, 27478568, 226753828, 1893462584, 15969598554, 135842638632, 1164075017512, 10039732285528, 87081507756245, 759128176746864, 6647475055207618, 58445784269830824, 515745587816906733
Offset: 0

Views

Author

Seiichi Manyama, Oct 16 2023

Keywords

Crossrefs

Cf. A176697, A366676.
Cf. A366267, A366558.

Programs

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

Formula

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

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

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