A143079 a(n) = ((9+sqrt(9))^n + (9-sqrt(9))^n)/2.

1, 9, 90, 972, 11016, 128304, 1516320, 18055872, 215830656, 2584929024, 30988915200, 371685583872, 4459138615296, 53503133036544, 641998414356480, 7703745879785472, 92443540002471936, 1109314016699940864, 13311717420420956160, 159740304365181468672, 1916881824302957592576

Offset

0,2

Comments

Equals A007318^9 * [1, 0, 9, 0, 81, 0, 729, ...]. - Gary W. Adamson, Oct 23 2008

Links

Paolo Xausa, Table of n, a(n) for n = 0..926

Index entries for linear recurrences with constant coefficients, signature (18,-72).

Formula

From Philippe Deléham, Oct 18 2008: (Start)

a(n) = 18*a(n-1) - 72*a(n-2).

a(n) = 6^n*(2^n+1)/2.

G.f.: (1-9*x)/(1-18*x+72*x^2). (End)

From R. J. Mathar, Oct 21 2008: (Start)

a(n) = (12^n + 6^n)/2.

G.f.: (1-9*x)/((1-12*x)*(1-6*x)). (End)

a(n) = 3^n*A007582(n) = (6^n+12^n)/2 = A000051(n)*A000079(n)*A000244(n)/2. - M. F. Hasler, Oct 22 2008

A007318^9 * [1, 0, 9, 0, 81, 0, 729, ...] produces this sequence. - Gary W. Adamson, Oct 23 2008

a(n) = Sum_{k=0..n} A098158(n,k)*9^k. - Philippe Deléham, Oct 23 2008

E.g.f.: exp(9*x)*cosh(3*x). - Elmo R. Oliveira, Jun 13 2026

Mathematica

LinearRecurrence[{18, -72}, {1, 9}, 25] (* Paolo Xausa, May 11 2026 *)

Prog

(PARI) A143079(n)=3^n*(1+1<<n)<<(n-1) \\ M. F. Hasler, Oct 22 2008

Crossrefs

Cf. A000051, A000079, A000244, A007318, A007582, A016175, A098158.

Sequence in context: A036258 A098399 A264914 * A233829 A165324 A082367

Adjacent sequences: A143076 A143077 A143078 * A143080 A143081 A143082

Keyword

nonn,easy,changed

Author

Al Hakanson (hawkuu(AT)gmail.com), Oct 15 2008

Extensions

Extended by R. J. Mathar and M. F. Hasler, Oct 21 2008

More terms from Paolo Xausa, May 11 2026

Status

approved