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.

A367048 G.f. satisfies A(x) = 1 + x*A(x)^4 + x^2*A(x).

Original entry on oeis.org

1, 1, 5, 27, 177, 1270, 9645, 76206, 619913, 5156959, 43667985, 375140383, 3261467573, 28641957520, 253702185717, 2263964868768, 20334261430769, 183680693283325, 1667613040080061, 15208587941854251, 139266058402655669, 1279953660931370623
Offset: 0

Views

Author

Seiichi Manyama, Nov 03 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n\2, binomial(3*n-5*k+1, k)*binomial(4*n-7*k, n-2*k)/(3*n-5*k+1));

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-5*k+1,k) * binomial(4*n-7*k,n-2*k)/(3*n-5*k+1).

A367049 G.f. satisfies A(x) = 1 + x*A(x)^4 + x^2*A(x)^2.

Original entry on oeis.org

1, 1, 5, 28, 187, 1361, 10479, 83914, 691738, 5830903, 50028259, 435454040, 3835732631, 34128555184, 306276957665, 2769050552948, 25197515469820, 230599623819217, 2121066298440282, 19597929365099640, 181814132152022195, 1692920612932871541
Offset: 0

Views

Author

Seiichi Manyama, Nov 03 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n\2, binomial(3*n-4*k+1, k)*binomial(4*n-6*k, n-2*k)/(3*n-4*k+1));

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-4*k+1,k) * binomial(4*n-6*k,n-2*k)/(3*n-4*k+1).

A367050 G.f. satisfies A(x) = 1 + x*A(x)^4 + x^2*A(x)^3.

Original entry on oeis.org

1, 1, 5, 29, 198, 1469, 11518, 93875, 787392, 6752175, 58929541, 521718814, 4674070602, 42296077935, 386027716280, 3549332631052, 32845586854208, 305685481682970, 2859315003009776, 26866125820982711, 253457922829307765, 2399910588283502630
Offset: 0

Views

Author

Seiichi Manyama, Nov 03 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n\2, binomial(3*n-3*k+1, k)*binomial(4*n-5*k, n-2*k)/(3*n-3*k+1));

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-3*k+1,k) * binomial(4*n-5*k,n-2*k)/(3*n-3*k+1).

A367040 G.f. satisfies A(x) = 1 + x^2 + x*A(x)^3.

Original entry on oeis.org

1, 1, 4, 15, 70, 360, 1953, 11008, 63837, 378390, 2282205, 13960890, 86411232, 540166219, 3405341160, 21625820793, 138216775785, 888371346825, 5738510504979, 37234351046835, 242567430368298, 1585979835198675, 10403866383915844, 68453912880893025
Offset: 0

Views

Author

Seiichi Manyama, Nov 03 2023

Keywords

Crossrefs

Programs

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

Formula

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

A367045 G.f. satisfies A(x) = 1 - x^2 + x*A(x)^4.

Original entry on oeis.org

1, 1, 3, 18, 112, 755, 5348, 39302, 296916, 2291861, 17997052, 143319918, 1154728056, 9395809374, 77099733884, 637298480966, 5301568498768, 44351526986704, 372890978840156, 3149155955471690, 26702387443603200, 227238745573918511, 1940201017862028108
Offset: 0

Views

Author

Seiichi Manyama, Nov 03 2023

Keywords

Crossrefs

Programs

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

Formula

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(3*(n-2*k)+1,k) * binomial(4*(n-2*k),n-2*k)/(3*(n-2*k)+1).
Showing 1-5 of 5 results.