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 A344491 a(n) = 1 + Sum_{k=0..n-4} binomial(n-3,k) * a(k). 4

%I #5 May 21 2021 08:07:08

%S 1,1,1,1,2,4,8,16,37,97,275,810,2468,7840,26182,92047,339029,1299185,

%T 5152244,21091816,89087652,388318264,1746324563,8094422821,

%U 38608318847,189179752492,950930369320,4898477508796,25841317224002,139534769647745,770795537345237,4353368099507329

%N a(n) = 1 + Sum_{k=0..n-4} binomial(n-3,k) * a(k).

%F G.f. A(x) satisfies: A(x) = (1 + x^3 * A(x/(1 - x))) / ((1 - x) * (1 + x^3)).

%t a[n_] := a[n] = 1 + Sum[Binomial[n - 3, k] a[k] , {k, 0, n - 4}]; Table[a[n], {n, 0, 31}]

%t nmax = 31; A[_] = 0; Do[A[x_] = (1 + x^3 A[x/(1 - x)])/((1 - x) (1 + x^3)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%Y Cf. A000629, A210541, A344489, A344490, A344492, A344493.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, May 21 2021

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Last modified August 8 08:46 EDT 2024. Contains 375018 sequences. (Running on oeis4.)