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.

A348878 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(2*x)).

Original entry on oeis.org

1, 1, 2, 5, 17, 74, 429, 3297, 34578, 495573, 9888497, 274123802, 10685538941, 583079000129, 44945515778914, 4867082587900837, 746167748281132753, 160981861948404281578, 49223569713040994430285, 21198824279482430844823713, 12946110661470835825027893426
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 02 2021

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 20; A[] = 0; Do[A[x] = 1/(1 - x - x^2 A[2 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
    a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[2^k a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 20}]

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-2} 2^k * a(k) * a(n-k-2).
a(n) ~ c * 2^(n*(n-2)/4), where c = 10.492153305884170498003413429333844276557493974205102819840538218355... - Vaclav Kotesovec, Nov 03 2021

A348879 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(3*x)).

Original entry on oeis.org

1, 1, 2, 6, 29, 221, 2815, 59607, 2175115, 134785987, 14543011028, 2682224473296, 864129873439979, 476879023670530355, 460188677448639450646, 761220053428592181980874, 2202591080616789155249254723, 10927081698418028875550581480027, 94836180093445711611212497662570806
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 02 2021

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 18; A[] = 0; Do[A[x] = 1/(1 - x - x^2 A[3 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
    a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[3^k a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 18}]

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-2} 3^k * a(k) * a(n-k-2).
a(n) ~ c * 3^(n*(n-2)/4), where c = 4.2101130581370834571021724998929772199905440992108887037121562184404379... - Vaclav Kotesovec, Nov 03 2021

A349037 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(-4*x)).

Original entry on oeis.org

1, 1, 2, -1, 29, 116, 7701, -103563, 31343898, 1759289595, 2057705197793, -457070362176172, 2156748187140412361, 1921405067209313680505, 36188075164863127910696914, -128870933294125665748520896793, 9713904752944734908048841134573557
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 06 2021

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 16; A[] = 0; Do[A[x] = 1/(1 - x - x^2 A[-4 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
    a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[(-4)^k a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 16}]

Formula

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