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.

A348861 G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(3*x))).

Original entry on oeis.org

1, 0, 1, 9, 253, 20754, 5064301, 3696964686, 8088964208893, 53079786931826952, 1044822534120774924517, 61696770693051062357722413, 10929459535778338593167921597497, 5808373834674826377471903826388912406, 9260429805605038398327449254849233420999649
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 02 2021

Keywords

Crossrefs

Cf. A005043, A015084, A348860, A348862.

Programs

  • Mathematica
    nmax = 14; A[] = 0; Do[A[x] = 1/((1 + x) (1 - x A[3 x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = (-1)^n + Sum[3^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]

Formula

a(n) = (-1)^n + Sum_{k=0..n-1} 3^k * a(k) * a(n-k-1).
a(n) ~ c * 3^(n*(n-1)/2), where c = 0.353669086629957226916356822657293915192042094460583129054709983118948... - Vaclav Kotesovec, Nov 02 2021

A348862 G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(4*x))).

Original entry on oeis.org

1, 0, 1, 16, 1041, 267552, 274242081, 1123570105392, 18409696460431921, 1206516278059945211200, 316282209730469497179053121, 331646250633753603369328903503952, 1391025527264722227030105092707830630481, 23337537123459992903665202300959789335795178848
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 02 2021

Keywords

Crossrefs

Cf. A005043, A015085, A348860, A348861.

Programs

  • Mathematica
    nmax = 13; A[] = 0; Do[A[x] = 1/((1 + x) (1 - x A[4 x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = (-1)^n + Sum[4^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]

Formula

a(n) = (-1)^n + Sum_{k=0..n-1} 4^k * a(k) * a(n-k-1).
a(n) ~ c * 2^(n*(n-1)), where c = 0.2554910592341818819974992745952574870516320592891123415106817713508566833... - Vaclav Kotesovec, Nov 02 2021

A348903 G.f. A(x) satisfies: A(x) = 1 / (1 - 2*x - x * A(2*x)).

Original entry on oeis.org

1, 3, 15, 123, 1623, 35427, 1349727, 94653195, 12690736167, 3325408581747, 1722610175806383, 1774299723226774683, 3644417103927252697335, 14949404433893216347632003, 122555228634241017164802041343, 2008680242472430855727593100321067
Offset: 0

Views

Author

Vaclav Kotesovec, Nov 03 2021

Keywords

Crossrefs

Cf. A348857, A348860, A348875, A348901, A348904.

Programs

  • Mathematica
    nmax = 20; A[] = 0; Do[A[x] = 1/(1 - 2*x - x*A[2*x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

a(n) ~ c * 2^(n*(n-1)/2), where c = 6*Product_{j>=1} (2^j+1)/(2^j-1) = 49.5359276146695003932648450...
a(0) = 1; a(n) = 2 * a(n-1) + Sum_{k=0..n-1} 2^k * a(k) * a(n-k-1). - Ilya Gutkovskiy, Nov 03 2021
Showing 1-3 of 3 results.

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

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