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.

A171206 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^6.

Original entry on oeis.org

1, 1, 12, 348, 19744, 2108784, 428817600, 169398274624, 131889504749568, 203937600707475456, 628561895904796999680, 3868208404121906515820544, 47571342639450113377565933568, 1169589733863427138021074362433536, 57499379103783344787572704263568097280, 5652994168279651703590653986228287051923456
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Crossrefs

Programs

  • Mathematica
    terms = 16; A[] = 0; Do[A[x] = 1+x*A[2x]^6 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^6); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_6>=0 and x_1+x_2+...+x_6=n-1} Product_{k=1..6} a(x_k). - Seiichi Manyama, Jul 08 2025

A171194 G.f. A(x) satisfies A(x) = 1/(1 - x*A(2*x)^4).

Original entry on oeis.org

1, 1, 9, 185, 7241, 525513, 71973193, 19054326985, 9916177373001, 10235479554015689, 21045100094428458057, 86370025530284981044937, 708236082282948046820221257, 11609413456993946896013575994313
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 15; A[] = 0; Do[A[x] = 1/(1 - x*A[2*x]^4) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Nov 03 2021 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1/(1-x*subst(A, x, 2*x)^4) ); polcoeff(A, n)}

Formula

a(n) ~ c * 2^(n*(n+3)/2), where c = 0.5726679317239416602436569686037310143000778... - Vaclav Kotesovec, Nov 03 2021
a(0) = 1; a(n) = 2^(n-1) * Sum_{i, j, k, l, m>=0 and i+j+k+l+m=n-1} (1/2)^i * a(i) * a(j) * a(k) * a(l) * a(m). - Seiichi Manyama, Jul 06 2025

A171196 G.f. A(x) satisfies A(x) = 1/(1 - x*A(2*x)^6).

Original entry on oeis.org

1, 1, 13, 397, 23261, 2532093, 520285021, 206632208765, 161306955003037, 249753449538341821, 770275887324912000733, 4741871606773351738426877, 58325180751309642789169099037, 1434100517517383561901937569640509
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 15; A[] = 0; Do[A[x] = 1/(1 - x*A[2*x]^6) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Nov 03 2021 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1/(1-x*subst(A, x, 2*x)^6) ); polcoeff(A, n)}

Formula

a(n) ~ c * 2^(n*(n+1)/2) * 3^n, where c = 0.363484431362432363073577975298028185297326... - Vaclav Kotesovec, Nov 03 2021
a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_7>=0 and x_1+x_2+...+x_7=n-1} (1/2)^x_1 * Product_{k=1..7} a(x_k). - Seiichi Manyama, Jul 06 2025
Showing 1-3 of 3 results.