A349185 G.f. A(x) satisfies: A(x) = (1 - x) / (1 - 2 * x - x^2 - x^2 * A(x)).

1, 1, 4, 11, 35, 111, 365, 1221, 4160, 14371, 50251, 177503, 632514, 2271027, 8208259, 29840993, 109049568, 400352639, 1475929092, 5461571729, 20279092033, 75531360153, 282123848574, 1056539226257, 3966214054639, 14922195004703, 56258116929483, 212505815364639, 804142811583006

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Formula

G.f.: (1 - 2*x - x^2 - sqrt(1 - 4*x - 2*x^2 + 8*x^3 + x^4)) / (2*x^2).

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

Mathematica

nmax = 28; A[_] = 0; Do[A[x_] = (1 - x)/(1 - 2 x - x^2 - x^2 A[x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
nmax = 28; CoefficientList[Series[(1 - 2 x - x^2 - Sqrt[1 - 4 x - 2 x^2 + 8 x^3 + x^4])/(2 x^2), {x, 0, nmax}], x]
a[0] = a[1] = 1; a[n_] := a[n] = 2 a[n - 1] + a[n - 2] + Sum[a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 28}]

Crossrefs

Cf. A056010, A085139, A086581, A128720, A349186.

Sequence in context: A295247 A052550 A197626 * A358826 A212910 A339034

Adjacent sequences: A349182 A349183 A349184 * A349186 A349187 A349188

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 09 2021

Status

approved