OFFSET
0,3
COMMENTS
Let A=[1,2,1;2,0,-2;1,-2,1] the 3 X 3 symmetric Krawtchouk matrix. Then a(n) is the 1,1 element of A^n.
REFERENCES
P. Feinsilver and J. Kocik, Krawtchouk matrices from classical and quantum walks, Contemporary Mathematics, 287 2001, pp. 83-96.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,8,-16).
FORMULA
a(n) = 2^((3*n-4)/2)*(1+(-1)^n)+2^(n-1).
a(n) = 2*a(n-1) + 8*a(n-2) - 16*a(n-3).
a(2n) = A081337(n) = (8^n+4^n)/2 and a(2n+1) = 4^n. - Peter Kagey, Jul 14 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 19 2004
STATUS
approved