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.

A360898 G.f. satisfies A(x) = 1 + x/(1 + x^3) * A(x/(1 + x^3)).

Original entry on oeis.org

1, 1, 1, 1, 0, -2, -5, -8, -5, 13, 57, 117, 110, -179, -1089, -2591, -2852, 4370, 30383, 77884, 88638, -165233, -1133248, -2963659, -3172087, 8519500, 53092522, 135857134, 122296383, -543728791, -2983007603, -7219203443, -4427302115, 40439842811, 194091075002
Offset: 0

Views

Author

Seiichi Manyama, Feb 25 2023

Keywords

Links

Crossrefs

Cf. A172385, A360899.
Cf. A360890.

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\3, (-1)^j*binomial(i-1-2*j, j)*v[i-3*j])); v;

Formula

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

A352865 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-k,k) * a(n-2*k-1).

Original entry on oeis.org

1, 1, 1, -1, -4, -5, 6, 36, 46, -101, -515, -506, 2554, 9991, 3067, -79915, -227056, 205681, 2841708, 5134140, -18296153, -107927240, -66578269, 1174691649, 4059143386, -4667894370, -69377504739, -126787267800, 669710503012, 3835079736835, 475781902203
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 06 2022

Keywords

Crossrefs

Cf. A014619, A172385, A352864.

Programs

  • Mathematica
    a[0] = 1; a[n_] := a[n] = Sum[(-1)^k Binomial[n - k, k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 30}]
nmax = 30; A[] = 0; Do[A[x] = 1 + x A[x/(1 + x^2)]/(1 + x^2)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]

Formula

G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 + x^2)) / (1 + x^2)^2.

A360899 G.f. satisfies A(x) = 1 + x/(1 + x^4) * A(x/(1 + x^4)).

Original entry on oeis.org

1, 1, 1, 1, 1, 0, -2, -5, -9, -13, -10, 10, 60, 155, 281, 325, 5, -1214, -4094, -8786, -12571, -5642, 35339, 149264, 363838, 596714, 417156, -1373639, -7048541, -18932245, -34095357, -29271979, 68706873, 413250742, 1193425228, 2293494882, 2201716631
Offset: 0

Views

Author

Seiichi Manyama, Feb 25 2023

Keywords

Crossrefs

Cf. A172385, A360898.
Cf. A360891.

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\4, (-1)^j*binomial(i-1-3*j, j)*v[i-4*j])); v;

Formula

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

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

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