OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,5).
FORMULA
G.f.: (1 + x)/(1 - 2*x - 5*x^2).
Equals INVERT transform of A026597: (1, 2, 6, 14, 38, 94,...).
a(n) = (1/6)*( -(1-sqrt(6))^n*sqrt(6) + sqrt(6)*(1+sqrt(6))^n + 3*(1-sqrt(6))^n + 3*(1 +sqrt(6))^n ). - Alexander R. Povolotsky, Aug 15 2010
EXAMPLE
a(5) = 443 = 2*a(4) + 5*a(3) = 2*129 + 5*37.
Using the INVERT operation, a(4) = 129 = (38, 14, 6, 2, 1) dot (1, 1, 3, 11, 37)
= (38 + 14 + 18 + 22 + 37); where A026597 = (1, 2, 6, 14, 38, 94,...).
MATHEMATICA
LinearRecurrence[{2, 5}, {1, 3}, 50] (* G. C. Greubel, Feb 18 2017 *)
PROG
(PARI) x='x+O('x^25); Vec((1 + x)/(1 - 2*x - 5*x^2)) \\ G. C. Greubel, Feb 18 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Aug 14 2010
STATUS
approved