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.

A348875 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(2*x)).

Original entry on oeis.org

1, 2, 8, 56, 656, 13184, 477248, 32524928, 4295916032, 1117098857984, 576442191401984, 592587279827787776, 1215991461595100598272, 4985567391504232291377152, 40861715233637664786276712448, 669641809249948891254213657460736, 21945501536426419427607885034600595456
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 02 2021

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 16; A[] = 0; Do[A[x] = 1/(1 - x - x 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 - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} 2^k * a(k) * a(n-k-1).
a(n) ~ c * 2^(n*(n-1)/2), where c = 1/(A048651 * A083864) = 2*Product_{j>=1} (2^j+1)/(2^j-1) = 16.51197587155650013108828169886454625305400323357646... - Vaclav Kotesovec, Nov 03 2021

A348877 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(4*x)).

Original entry on oeis.org

1, 2, 12, 232, 15792, 4108192, 4223439552, 17316156716672, 283777228606348032, 18598759772257600748032, 4875627680189345535622228992, 5112485673116229482189477259405312, 21443339558695300334256395183459423465472, 359759625310995318218730673236935427042834358272
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 02 2021

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 13; A[] = 0; Do[A[x] = 1/(1 - x - x 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 - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} 4^k * a(k) * a(n-k-1).
a(n) ~ c * 2^(n*(n-1)), where c = 2*Product_{j>=1} (4^j+1)/(4^j-1) = 3.938520707336538863894387393934531340132379924622409970534801850699757421... - Vaclav Kotesovec, Nov 03 2021

A349033 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(-3*x)).

Original entry on oeis.org

1, 2, -2, -34, 826, 70634, -16895162, -12385295242, 27037369868722, 177500531682526034, -3493033395457140741746, -206274103942288894158940594, 36540013650535335202759969693162, 19419007557809179132528500713950083002, -30960092711143410415029705970483650552421802
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 06 2021

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 14; A[] = 0; Do[A[x] = 1/(1 - x - x 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 - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]

Formula

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