A054459 A001333(n), n >= 1, convolved with itself.

1, 6, 23, 76, 233, 682, 1935, 5368, 14641, 39406, 104935, 276996, 725849, 1890258, 4896415, 12624752, 32419297, 82951766, 211573047, 538086716, 1364974409, 3454480250, 8724052271, 21989264232, 55326056977, 138975010110

Offset: 0

Author

Wolfdieter Lang, Apr 26 2000

Keywords

• easy
• nonn

Comments

a(n) = A054458(n+1,1) (second column of convolution triangle).

References

• R. P. Grimaldi, Ternary strings with no consecutive 0's and no consecutive 1's, Congressus Numerantium, 205 (2011), 129-149. (The sequence t_n, also the sequence lev_{n-1}.)

Links

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

Crossrefs

Cf. A054458, A001333, A002203.

Programs

Mathematica

LinearRecurrence[{4, -2, -4, -1}, {1, 6, 23, 76}, 30] (* Paolo Xausa, Feb 06 2024 *)

Formula

a(n) = ((4*n+3)*LP(n)+(2*n+1)*LP(n-1))/4, n >= 1, with LP(n) = A001333(n+1), a(0) = 1.

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

a(n) = 2*A006645(n+2) - A000129(n+1). - R. J. Mathar, Feb 05 2024