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

Offset: 0

Author

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

Keywords

• nonn

Comments

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

Links

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

Programs

PARI

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

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

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

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

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

Extensions

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