OFFSET
0,5
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-4,1,-5,4).
FORMULA
a(n) = a(n-3) + (4^(n-2) - 1)/3.
a(n) = 1/3 * Sum_{k=0..n} floor(4^k/21) = Sum_{k=0..n} floor(4^k/63).
a(n) = 5*a(n-1) - 4*a(n-2) + a(n-3) - 5*a(n-4) + 4*a(n-5).
G.f.: x^3/((1-x) * (1-4*x) * (1-x^3)).
a(n) = (floor(4^(n+1)/63) - floor((n+1)/3))/3.
PROG
(PARI) a(n, m=3, k=4) = (k^(n+1)\(k^m-1)-(n+1)\m)/(k-1);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 22 2023
STATUS
approved