A387652 a(n) = Sum_{k=0..floor(n/3)} 2^(n-3*k) * binomial(2*k+1,2*n-6*k+1).

1, 0, 0, 3, 2, 0, 5, 20, 4, 7, 70, 84, 17, 168, 504, 299, 346, 1848, 2653, 1452, 5180, 13743, 12350, 14508, 51561, 81440, 68432, 162323, 391026, 442544, 555445, 1498116, 2500276, 2666711, 5202550, 11465284, 14985153, 20025432, 45011176, 77173371, 95454666, 168802152

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1500

Index entries for linear recurrences with constant coefficients, signature (0,0,2,4,0,-1,4,-4).

Formula

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

a(n) = 2*a(n-3) + 4*a(n-4) - a(n-6) + 4*a(n-7) - 4*a(n-8).

Mathematica

Table[Sum[2^(n-3*k)*Binomial[2*k+1, 2*n-6*k+1], {k, 0, Floor[n/3]}], {n, 0, 40}] (* Vincenzo Librandi, Sep 05 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, 2^(n-3*k)*binomial(2*k+1, 2*n-6*k+1));
(Magma) [&+[2^(n-3*k)* Binomial(2*k+1, 2*n-6*k+1): k in [0..Floor (n/3)]]: n in [0..40]]; // Vincenzo Librandi, Sep 05 2025

Crossrefs

Cf. A387627, A387651.

Cf. A387648.

Sequence in context: A359843 A364361 A338022 * A253176 A079408 A114376

Adjacent sequences: A387649 A387650 A387651 * A387653 A387654 A387655

Keyword

nonn

Author

Seiichi Manyama, Sep 05 2025

Status

approved