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 1-4 of 4 results.

A171192 G.f. satisfies A(x) = 1/(1 - x*A(2x)^2).

Original entry on oeis.org

1, 1, 5, 53, 1045, 37941, 2596693, 343615093, 89402126741, 46139256172725, 47433024462021589, 97333484052884523765, 399068205440018335950357, 3270764880283567936326235445, 53601302478763156422575938811989
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Links

Crossrefs

Cf. A015083, A171193-A171198.

Programs

  • Mathematica
    nmax = 15; A[] = 0; Do[A[x] = 1/(1 - x*A[2*x]^2) + 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)^2) ); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = Sum_{i=0..n-1} Sum_{j=0..n-i-1} 2^(i+j) * a(i) * a(j) * a(n-i-j-1). - Ilya Gutkovskiy, Nov 03 2021
a(n) ~ c * 2^(n*(n+1)/2), where c = 1.3216968146657309382653061124105846042506... - Vaclav Kotesovec, Nov 03 2021

A171202 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^4.

Original entry on oeis.org

1, 1, 8, 152, 5664, 399376, 53846016, 14141384704, 7330134466560, 7551251740344320, 15510852680588984320, 63626087316632048238592, 521607805205244557347782656, 8549156556447111748331767857152, 280190094729160875643888549840814080, 18364219805837823940403573170370661842944
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Links

Crossrefs

Cf. A135867, A171200, A171201, A171203, A171204-A171211, A343439.
Cf. A143047, A171193.

Programs

  • Mathematica
    terms = 16; A[] = 0; Do[A[x] = 1 + x*A[2x]^4 + 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)^4); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{i, j, k, l>=0 and i+j+k+l=n-1} a(i) * a(j) * a(k) * a(l). - 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

Links

Crossrefs

Cf. A015083, A171192, A171193, A171195-A171198.

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

A385649 G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(x) + A(2*x))^3 ).

Original entry on oeis.org

1, 8, 352, 29696, 4263424, 1049470976, 462206058496, 380751228633088, 605491779706159104, 1892234112450731442176, 11725274627114715154743296, 144692808471111027067403108352, 3563512028948515548768609167736832, 175339259291213196115801459160952864768
Offset: 0

Views

Author

Seiichi Manyama, Jul 06 2025

Keywords

Crossrefs

Cf. A385617, A385648.
Cf. A171193, A385651.

Formula

a(0) = 1; a(n) = Sum_{i, j, k, l>=0 and i+j+k+l=n-1} (2^j+1) * (2^k+1) * (2^l+1) * a(i) * a(j) * a(k) * a(l).
Showing 1-4 of 4 results.

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

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