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.

A364625 G.f. satisfies A(x) = 1/(1-x)^3 + x^2*A(x)^2.

Original entry on oeis.org

1, 3, 7, 16, 38, 95, 249, 678, 1901, 5451, 15906, 47066, 140868, 425657, 1296665, 3977684, 12276617, 38094013, 118768915, 371875752, 1168843808, 3686549845, 11664123048, 37011249678, 117750111763, 375529083267, 1200327617200, 3844662925222, 12338289374046
Offset: 0

Views

Author

Seiichi Manyama, Jul 30 2023

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(2/((1-x)^3*(1+sqrt(1-4*x^2/(1-x)^3))))

Formula

G.f.: A(x) = 2 / ( (1-x)^3 * (1 + sqrt( 1 - 4*x^2/(1-x)^3 )) ).
a(n) = Sum_{k=0..floor(n/2)} binomial(n+k+2,3*k+2) * binomial(2*k,k) / (k+1).

A364627 G.f. satisfies A(x) = 1/(1-x)^3 + x^2*A(x)^4.

Original entry on oeis.org

1, 3, 7, 22, 97, 469, 2339, 12148, 65295, 358979, 2006977, 11380702, 65311575, 378574425, 2213092750, 13032826536, 77244242937, 460413902079, 2758088752351, 16596379614234, 100269075879881, 607996092039949, 3698873710967989, 22570809986322440
Offset: 0

Views

Author

Seiichi Manyama, Jul 30 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n\2, binomial(n+7*k+2, 9*k+2)*binomial(4*k, k)/(3*k+1));

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(n+7*k+2,9*k+2) * binomial(4*k,k) / (3*k+1).

A369691 G.f. satisfies A(x) = 1/(1-x)^3 + x^3*A(x)^3.

Original entry on oeis.org

1, 3, 6, 11, 24, 66, 196, 576, 1692, 5110, 15933, 50604, 161988, 521700, 1693362, 5541679, 18260055, 60487659, 201272437, 672550158, 2256204327, 7596059333, 25655943417, 86904524289, 295154911774, 1004906765178, 3429178160346, 11726499288028, 40178538608682
Offset: 0

Views

Author

Seiichi Manyama, Jan 29 2024

Keywords

Crossrefs

Programs

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

Formula

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