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 1-2 of 2 results.

A367042 G.f. satisfies A(x) = 1 + x^3 + x*A(x)^2.

Original entry on oeis.org

1, 1, 2, 6, 16, 48, 152, 500, 1688, 5816, 20368, 72288, 259424, 939808, 3432192, 12622416, 46706144, 173762016, 649569216, 2438748864, 9191656192, 34765298944, 131912452864, 501987944832, 1915417307392, 7326620001536, 28088736525824, 107913607531520
Offset: 0

Views

Author

Seiichi Manyama, Nov 03 2023

Keywords

Crossrefs

Programs

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

Formula

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

A367047 G.f. satisfies A(x) = 1 - x^3 + x*A(x)^4.

Original entry on oeis.org

1, 1, 4, 21, 136, 941, 6864, 52006, 405312, 3228654, 26170764, 215166638, 1789998808, 15040070843, 127450104568, 1087988783356, 9347556057040, 80766068931498, 701359680126592, 6117887649100980, 53581405635501276, 470988258063461393
Offset: 0

Views

Author

Seiichi Manyama, Nov 03 2023

Keywords

Crossrefs

Programs

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

Formula

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