A349186 G.f. A(x) satisfies: A(x) = (1 - x) / (1 - 2 * x - x^2 - x^3 * A(x)).

1, 1, 3, 8, 21, 57, 157, 438, 1237, 3530, 10165, 29505, 86243, 253654, 750157, 2229469, 6655369, 19946979, 60000443, 181076982, 548125929, 1663786344, 5063133335, 15444046031, 47211447131, 144614092732, 443803262627, 1364370846941, 4201333752921, 12957168021207

Offset

0,3

Links

Table of n, a(n) for n=0..29.

Formula

G.f.: (1 - 2*x - x^2 - sqrt(1 - 4*x + 2*x^2 + 5*x^4)) / (2*x^3).

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

Mathematica

nmax = 29; A[_] = 0; Do[A[x_] = (1 - x)/(1 - 2 x - x^2 - x^3 A[x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
nmax = 29; CoefficientList[Series[(1 - 2 x - x^2 - Sqrt[1 - 4 x + 2 x^2 + 5 x^4])/(2 x^3), {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 - 3], {k, 0, n - 3}]; Table[a[n], {n, 0, 29}]

Crossrefs

Cf. A002026, A004148, A086581, A217333, A349185.

Sequence in context: A006835 A014318 A158495 * A273720 A018037 A018038

Adjacent sequences: A349183 A349184 A349185 * A349187 A349188 A349189

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 09 2021

Status

approved