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 1-4 of 4 results.

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

A348880 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(4*x)).

Original entry on oeis.org

1, 1, 2, 7, 45, 540, 12645, 578965, 52968266, 9592378291, 3490570329073, 2521575506955308, 3665174976025818601, 10583587128179171478201, 61512603105342112799632050, 710375545029057279438117199695, 16513584476995892580457952423234565
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 02 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).
a(n) ~ c * 2^(n*(n-2)/2), where c = 3.18049189724646501466385558274654521200715578089919192312230814532162... - Vaclav Kotesovec, Nov 03 2021

A349035 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(-2*x)).

Original entry on oeis.org

1, 1, 2, 1, 9, 6, 165, 97, 10970, 8617, 2838793, 1206206, 2912348749, 3338391105, 11938619074866, -3485058191151, 195607339607544393, 505337929567029942, 12820529140255160177781, -40595263531274884237983, 3360756421633193695872693450
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 06 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).

A349013 G.f. A(x) satisfies: A(x) = (1 + x * A(2*x)) / (1 - x^2 * A(x)).

Original entry on oeis.org

1, 1, 3, 14, 119, 1938, 62291, 3990822, 510954584, 130812494690, 66977027614263, 68584738950054184, 140461679588587238360, 575331176899085656611498, 4713113282218244019907299347, 77219649166807400596911172015640, 2530333473325322974256848862067093128
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 05 2021

Keywords

Crossrefs

Programs

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

Formula

a(0) = 1; a(n) = 2^(n-1) * a(n-1) + Sum_{k=0..n-2} a(k) * a(n-k-2).
a(n) ~ c * 2^(n*(n-1)/2), where c = 1.903611332661849505687584024897203124045921097899485586512432930506328189... - Vaclav Kotesovec, Nov 06 2021
Showing 1-4 of 4 results.