A152106 a(n) = (11^n + 7^n)/2.

1, 9, 85, 837, 8521, 88929, 944605, 10155357, 110061841, 1199150649, 13109949925, 143644498677, 1576134831961, 17309800577169, 190214028328045, 2090997865462797, 22991481397070881, 252839829506640489, 2780772863545070965, 30585244671799959717, 336414893599428810601

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Nov 24 2008

Keywords

• nonn
• easy

Examples

			a(3) = (11^3 + 7^3)/2 = 837.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..960
• Index entries for linear recurrences with constant coefficients, signature (18,-77).

Crossrefs

Cf. A098158.

Programs

Mathematica

LinearRecurrence[{18,-77},{1,9},30] (* Harvey P. Dale, Jan 26 2025 *)

PARI

a(n)=(11^n+7^n)/2 \\ Charles R Greathouse IV, Aug 23 2024

Formula

a(n) = ((9 + sqrt(4))^n + (9 - sqrt(4))^n)/2.

From Philippe Deléham, Nov 26 2008: (Start)

a(n) = 18*a(n-1) - 77*a(n-2), n > 1; a(0)=1, a(1)=9.

G.f.: (1-9*x)/(1-18*x+77*x^2).

a(n) = (1/9^n)*Sum_{k=0..n} A098158(n,k)*9^(2*k)*4^(n-k). (End)

E.g.f.: exp(9*x)*cosh(2*x). - Elmo R. Oliveira, Aug 23 2024

Extensions

Extended beyond a(6) by Klaus Brockhaus, Nov 26 2008

More terms by Elmo R. Oliveira, Aug 23 2024