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

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

A349036 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(-3*x)).

Original entry on oeis.org

1, 1, 2, 0, 17, 29, 1459, -4233, 1056763, 11355763, 6957281732, -209598234798, 410408244241271, 37950250148465939, 218184080600974976674, -60068553848055713514168, 1043447774597599997266176403, 864004926526955255880635472763, 44918734284964096829849186288888390
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 06 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).
Showing 1-3 of 3 results.