A376695 a(n) = Sum_{k=0..floor(n/2)} binomial(n-2*k,floor(k/3)).

1, 1, 2, 2, 3, 3, 3, 4, 5, 7, 9, 12, 15, 18, 22, 27, 34, 43, 55, 70, 88, 110, 137, 171, 214, 269, 339, 427, 537, 674, 845, 1059, 1328, 1667, 2094, 2631, 3305, 4150, 5209, 6537, 8204, 10298, 12929, 16234, 20384, 25593, 32130, 40334, 50632, 63561, 79795, 100179, 125772, 157902, 198236

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: (1-x^6)/((1-x^2) * (1-x*(1+x^6))) = (1+x^2+x^4)/(1-x*(1+x^6)).

a(n) = a(n-1) + a(n-7).

a(n) = A005709(n) + A005709(n-2) + A005709(n-4).

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 1}, {1, 1, 2, 2, 3, 3, 3}, 60] (* Harvey P. Dale, Mar 20 2026 *)

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(n-2*k, k\3));
(PARI) my(N=60, x='x+O('x^N)); Vec((1+x^2+x^4)/(1-x*(1+x^6)))

Crossrefs

Cf. A000930, A098523.

Cf. A005709.

Sequence in context: A003105 A240856 A081166 * A173910 A036846 A227396

Adjacent sequences: A376692 A376693 A376694 * A376696 A376697 A376698

Keyword

nonn

Author

Seiichi Manyama, Oct 01 2024

Status

approved