A089931 a(n) = 3*a(n-1) + 3*a(n-3) + a(n-4).

1, 3, 9, 30, 100, 330, 1089, 3597, 11881, 39240, 129600, 428040, 1413721, 4669203, 15421329, 50933190, 168220900, 555595890, 1835008569, 6060621597, 20016873361, 66111241680, 218350598400, 721163036880, 2381839709041

Offset

0,2

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1927

Andreas M. Hinz and Paul K. Stockmeyer, Precious Metal Sequences and Sierpinski-Type Graphs, J. Integer Seq., Vol 25 (2022), Article 22.4.8.

Index entries for sequences related to Chebyshev polynomials.

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

Formula

a(n) = ((3 + sqrt(13)^n(11 + 3*sqrt(13))/13 + (3 - sqrt(13)^n(11 - 3*sqrt(13))/13)*2^(-1 - n) + 2(-1)^n/13;

a(n) = (-i)^n*Sum_{k=0..floor(n/2)} U(n-2k, 3i/2) where i = sqrt(-1).

G.f.: -1 / ( (1+x^2)*(x^2+3*x-1) ). - R. J. Mathar, Feb 14 2015

Mathematica

LinearRecurrence[{3, 0, 3, 1}, {1, 3, 9, 30}, 30] (* Harvey P. Dale, Jun 16 2015 *)

Crossrefs

Cf. A006498.

Sequence in context: A102898 A050181 A275690 * A148946 A096222 A148947

Adjacent sequences: A089928 A089929 A089930 * A089932 A089933 A089934

Keyword

easy,nonn

Author

Paul Barry, Nov 15 2003

Status

approved