A376735 a(n) = Sum_{k=0..floor(n/4)} (n-3*k+1) * binomial(n-3*k,k)^2.

1, 2, 3, 4, 7, 18, 43, 88, 162, 298, 583, 1188, 2402, 4722, 9123, 17648, 34463, 67632, 132382, 257748, 500244, 970790, 1885815, 3663816, 7110990, 13783264, 26692422, 51672484, 100007876, 193487262, 374149235, 723110880, 1396927383, 2697694410, 5208058825

Offset

0,2

Links

Table of n, a(n) for n=0..34.

Formula

G.f.: (1-x-x^4)/((1-x-x^4)^2 - 4*x^5)^(3/2).

D-finite with recurrence 4*n*(2*n-3)*a(n) +(-22*n^2+43*n-13)*a(n-1) +2*(10*n^2-26*n+15)*a(n-2) -3*(n-1)*(2*n-5)*a(n-3) +8*(-2*n^2-n+16)*a(n-4) +2*(-2*n^2-23*n-15)*a(n-5) +12*(n-1)^2*a(n-6) +4*n*(2*n+5)*a(n-8) -3*(2*n+1)*(n-1)*a(n-9)=0. - R. J. Mathar, Oct 17 2024

Prog

(PARI) a(n) = sum(k=0, n\4, (n-3*k+1)*binomial(n-3*k, k)^2);

Crossrefs

Cf. A182884, A375565.

Cf. A246883.

Sequence in context: A338928 A110705 A139439 * A352902 A119330 A373392

Adjacent sequences: A376732 A376733 A376734 * A376736 A376737 A376738

Keyword

nonn

Author

Seiichi Manyama, Oct 17 2024

Status

approved