A352039 - OEIS

A352039

a(0) = 1; a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * a(k).

1, 1, 1, 2, 3, 4, 6, 9, 13, 20, 32, 51, 82, 133, 215, 346, 555, 886, 1408, 2231, 3528, 5572, 8797, 13892, 21950, 34707, 54919, 86958, 137761, 218339, 346178, 549073, 871261, 1383243, 2197542, 3494019, 5560580, 8858687, 14128865, 22560717, 36067022, 57725840

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..41.

FORMULA

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

MATHEMATICA

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 2 k, k] a[k], {k, 0, Floor[n/3]}]; Table[a[n], {n, 0, 41}]

nmax = 41; A[_] = 1; Do[A[x_] = A[x^3/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

CROSSREFS

Cf. A092684, A102547, A352041.