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 1-5 of 5 results.

A348876 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(3*x)).

Original entry on oeis.org

1, 2, 10, 122, 3778, 321794, 79518154, 58289895290, 127713856067074, 838441945709583746, 16506407616569722560778, 974752895709158578160969978, 172678450359956040815290930278850, 91769099059347441553324620759011469698, 146309952397373808216450794120154608358754762
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 02 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).
a(n) ~ c * 3^(n*(n-1)/2), where c = 2*Product_{j>=1} (3^j+1)/(3^j-1) = QPochhammer(-1, 1/3) / QPochhammer(1/3) = 5.58779203552209791475992929265... - 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

A349032 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(-2*x)).

Original entry on oeis.org

1, 2, 0, -8, 48, 1024, -29376, -2008960, 249483264, 64889376256, -32966832018432, -33890678261809152, 69272943033878630400, 284019472607289480388608, -2325552273529676473281282048, -38111154065733485540332985155584, 1248673879720871231428642700812025856
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 06 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).

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

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

A349012 G.f. A(x) satisfies: A(x) = (1 + x * A(2*x)) / (1 - x * A(x)).

Original entry on oeis.org

1, 2, 8, 52, 552, 10208, 350112, 23159760, 3012389984, 777296223040, 399542726439936, 409933997609848192, 840366306053838941952, 3443822768422065940362240, 28218687132517064788995222528, 462391421142204650963524251763968, 15152566983759983965941543133445666304
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 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 - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]

Formula

a(0) = 1; a(n) = 2^(n-1) * a(n-1) + Sum_{k=0..n-1} a(k) * a(n-k-1).
a(n) ~ c * 2^(n*(n-1)/2), where c = 11.40022022373995418911523299051117421707893086825818379118899572625286143... - Vaclav Kotesovec, Nov 06 2021
Showing 1-5 of 5 results.