A373638 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-5*k,k).

1, 1, 2, 5, 9, 21, 43, 92, 196, 414, 882, 1869, 3970, 8427, 17887, 37975, 80608, 171121, 363254, 771119, 1636944, 3474913, 7376591, 15659094, 33241289, 70564951, 149795989, 317988473, 675029164, 1432958824, 3041899638, 6457375642, 13707783053, 29099021980

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,3,0,-3,0,1).

Formula

G.f.: 1 / (1 - x^2 - x/(1 - x^2)^2).

a(n) = a(n-1) + 3*a(n-2) - 3*a(n-4) + a(n-6) for n > 5.

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(3*n-5*k, k));

Crossrefs

Cf. A000045, A052535.

Sequence in context: A097163 A117186 A155042 * A001851 A356375 A303963

Adjacent sequences: A373635 A373636 A373637 * A373639 A373640 A373641

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 12 2024

Status

approved