OFFSET
0,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..960
Index entries for linear recurrences with constant coefficients, signature (18,-77).
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
EXAMPLE
a(3) = (11^3 + 7^3)/2 = 837.
MATHEMATICA
LinearRecurrence[{18, -77}, {1, 9}, 30] (* Harvey P. Dale, Jan 26 2025 *)
PROG
(PARI) a(n)=(11^n+7^n)/2 \\ Charles R Greathouse IV, Aug 23 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Nov 24 2008
EXTENSIONS
Extended beyond a(6) by Klaus Brockhaus, Nov 26 2008
More terms by Elmo R. Oliveira, Aug 23 2024
STATUS
approved