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

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

A349034 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(-4*x)).

Original entry on oeis.org

1, 2, -4, -88, 5360, 1395104, -1423111744, -5834786588032, 95573832673124096, 6263909110244685920768, -1642021136070472933898232832, -1721790522986063937046243536001024, 7221705990593287793620261453916626546688, 121160150179535955805047509278599956409746825216
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 06 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).
Showing 1-3 of 3 results.