OFFSET
0,2
COMMENTS
Let A=[1,1,1,1;3,1,-1,-3;3,-1,-1,3;1,-1,1,-1], the 4 X 4 Krawtchouk matrix. Then a(n)=trace((A*A')^n)/4.
Twelfth binomial transform of ((4*sqrt(5))^n +(-4*sqrt(5))^n)/2, with g.f. 1/(1-80*x^2).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (24,-64).
FORMULA
G.f.: (1-12*x)/(1-24*x+64*x^2).
a(n) = ((12+4*sqrt(5))^n+(12-4*sqrt(5))^n)/2.
a(n) = 2^(n-1)*((sqrt(5)-1)^(2*n)+(sqrt(5)+1)^(2*n)).
a(n) = 4^n*A098648(n). - R. J. Mathar, Nov 11 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 18 2004
STATUS
approved