A054460 A001333(n), n >= 1, convolved twice with itself.

1, 9, 48, 204, 765, 2649, 8680, 27312, 83313, 247985, 723624, 2077164, 5880797, 16454865, 45577200, 125130432, 340882113, 922265721, 2479938368, 6631802220, 17646603933, 46744464745, 123314065944, 324085913136, 848801213425

Offset

0,2

Comments

a(n) = A054458(n+2,2) (third column of convolution triangle).

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (6,-9,-4,9,6,1)

Formula

a(n) = (n+1)*(LP2(n+1)+2*LP2(n)+LP2(n-1))/8, n >= 1, LP2(n) = A054459(n), a(0) = 1.

a(n) = (n+1)*((10*n+11)*LP(n)+(4*n+5)*LP(n-1))/16, n >= 1, LP(n) = A001333(n+1).

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

a(n) = +6*a(n-1) -9*a(n-2) -4*a(n-3) +9*a(n-4) +6*a(n-5) +a(n-6). - R. J. Mathar, Feb 05 2024

Mathematica

LinearRecurrence[{6, -9, -4, 9, 6, 1}, {1, 9, 48, 204, 765, 2649}, 30] (* Paolo Xausa, Feb 06 2024 *)

Crossrefs

Cf. A054458, A054459, A001333, A002203.

Sequence in context: A018984 A055582 A359175 * A115053 A181959 A171011

Adjacent sequences: A054457 A054458 A054459 * A054461 A054462 A054463

Keyword

easy,nonn

Author

Wolfdieter Lang, Apr 26 2000

Status

approved