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A352042 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-2*k-1,k) * a(k). 1
1, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 61, 93, 144, 226, 359, 574, 920, 1475, 2361, 3769, 6000, 9528, 15100, 23897, 37789, 59739, 94446, 149365, 236322, 374073, 592357, 938311, 1486625, 2355620, 3732704, 5914682, 9371599, 14847866, 23522460, 37262742, 59026662 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
G.f. A(x) satisfies: A(x) = 1 + x * A(x^3/(1 - x)) / (1 - x).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 2 k - 1, k] a[k], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 43}]
nmax = 43; A[_] = 0; Do[A[x_] = 1 + x A[x^3/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
Sequence in context: A135851 A199804 A101913 * A121653 A238434 A061418
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 01 2022
STATUS
approved

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Last modified April 13 20:16 EDT 2024. Contains 371645 sequences. (Running on oeis4.)