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 1-4 of 4 results.

A366555 G.f. A(x) satisfies A(x) = 1 + x + x^3*A(x)^3.

Original entry on oeis.org

1, 1, 0, 1, 3, 3, 4, 15, 30, 42, 99, 255, 475, 915, 2232, 4977, 9945, 21945, 51093, 110634, 238005, 542341, 1227390, 2696841, 6035886, 13770402, 31001133, 69485295, 157945293, 359888373, 814699002, 1850816823, 4231092060, 9659302380, 22028018679
Offset: 0

Views

Author

Seiichi Manyama, Oct 13 2023

Keywords

Crossrefs

Cf. A019497, A366266, A366556.
Cf. A366591.

Programs

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

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*k+1,n-3*k) * binomial(3*k,k)/(2*k+1).
a(n) = A366591(n) + A366591(n-1).

A366592 G.f. A(x) satisfies A(x) = 1 + x^4*(1+x)^2*A(x)^3.

Original entry on oeis.org

1, 0, 0, 0, 1, 2, 1, 0, 3, 12, 18, 12, 15, 72, 180, 240, 235, 512, 1552, 3080, 4123, 5810, 13825, 33200, 58813, 85932, 151578, 346920, 726897, 1242234, 2025177, 3952704, 8509875, 16525872, 28565064, 50849280, 102266019, 208932438, 391951131, 699037248, 1313756457
Offset: 0

Views

Author

Seiichi Manyama, Oct 14 2023

Keywords

Crossrefs

Cf. A366221, A366590, A366591.
Cf. A366556.

Programs

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

Formula

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

A366594 G.f. A(x) satisfies A(x) = 1 + x^3*(1+x)^3*A(x)^4.

Original entry on oeis.org

1, 0, 0, 1, 3, 3, 5, 24, 60, 102, 258, 816, 1992, 4452, 12012, 33617, 84627, 212823, 577361, 1561077, 4063059, 10715009, 29052015, 78235107, 208358693, 560561391, 1522609569, 4120277283, 11129752269, 30240233739, 82441619605, 224488878600, 611770878012
Offset: 0

Views

Author

Seiichi Manyama, Oct 14 2023

Keywords

Crossrefs

Cf. A366272, A366593, A366595.
Cf. A366588, A366591.
Cf. A366557.

Programs

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

Formula

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

A366590 G.f. A(x) satisfies A(x) = 1 + x^2*(1+x)^2*A(x)^3.

Original entry on oeis.org

1, 0, 1, 2, 4, 12, 30, 84, 238, 680, 1993, 5882, 17575, 52976, 160870, 491924, 1512940, 4677672, 14529744, 45320640, 141897039, 445792908, 1404899598, 4440113940, 14069493813, 44689897200, 142268117566, 453839997836, 1450547245960, 4644492976232, 14896047099592
Offset: 0

Views

Author

Seiichi Manyama, Oct 14 2023

Keywords

Crossrefs

Cf. A366221, A366591, A366592.
Cf. A019497.

Programs

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

Formula

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

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

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