OFFSET
1,1
COMMENTS
If p is an odd prime, a((p+1)/2) == 2 mod p. In other words, a((p+1)/2) - 2^p is divisible by p where p is an odd prime.
LINKS
Colin Barker, Table of n, a(n) for n = 1..950
Index entries for linear recurrences with constant coefficients, signature (12,-16).
FORMULA
a(n) = 12*a(n-1) - 16*a(n-2) for n>2. G.f.: 2*x*(1+4*x) / (1-12*x+16*x^2). - Colin Barker, Mar 17 2016
a(n) = (1+sqrt(5))^(2*n-1) + (1-sqrt(5))^(2*n-1).
EXAMPLE
a(2) = 32 because (1 + sqrt(5))^3 + (1 - sqrt(5))^3 = 32.
PROG
(PARI) Vec(2*x*(1+4*x)/(1-12*x+16*x^2) + O(x^50)) \\ Colin Barker, Mar 17 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Altug Alkan, Mar 17 2016
STATUS
approved