A349038 -id:A349038 - cp's OEIS frontend

A349045 G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(-3*x)).

1, 1, -5, -101, 5293, 869269, -420787937, -614362594985, 2685998620138297, 35251053957604379689, -1387622522805833315933693, -163878220402091372424795125261, 58060742480730955957157145945031525, 61711834213019891772066352604323845604861

Offset: 0

Ilya Gutkovskiy, Nov 06 2021

sign

Cf. A001003, A015098, A348188, A349038, A349046.

nmax = 13; A[] = 0; Do[A[x] = 1/(1 + x - 2 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] + 2 Sum[(-3)^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]

a(0) = 1; a(n) = -a(n-1) + 2 * Sum_{k=0..n-1} (-3)^k * a(k) * a(n-k-1).

A349046 G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(-4*x)).

Original entry on oeis.org

1, 1, -7, -239, 30185, 15518977, -31752293287, -260178568173071, 8525011498792301513, 1117407361630407158712289, -585841036144574163016069731271, -1228598872333737909217248906305521967, 10306231872061986643099600924851012311829929

Offset: 0

Ilya Gutkovskiy, Nov 06 2021

sign

Cf. A001003, A015099, A348902, A349038, A349045.

nmax = 12; A[] = 0; Do[A[x] = 1/(1 + x - 2 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] + 2 Sum[(-4)^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 12}]

a(0) = 1; a(n) = -a(n-1) + 2 * Sum_{k=0..n-1} (-4)^k * a(k) * a(n-k-1).

cp's OEIS Frontend

A349045 G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(-3*x)).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula