OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,26,0,-25).
FORMULA
a(n) = (5^n - 1)/(2^(3 - (n mod 2))).
From Colin Barker, Nov 16 2015: (Start)
a(n) = (5^n-1)/8 for n even.
a(n) = (5^n-1)/4 for n odd.
a(n) = 26*a(n-2)-25*a(n-4) for n>3.
G.f.: x*(5*x^2+3*x+1) / ((x-1)*(x+1)*(5*x-1)*(5*x+1)).
(End)
MATHEMATICA
a[n_] := (5^n - 1)/(2^(3 - Mod[n, 2]));
Table[a[n], {n, 0, 30}]
LinearRecurrence[{0, 26, 0, -25}, {0, 1, 3, 31}, 30] (* Harvey P. Dale, Aug 05 2018 *)
PROG
(PARI) concat(0, Vec(x*(5*x^2+3*x+1) / ((x-1)*(x+1)*(5*x-1)*(5*x+1)) + O(x^30))) \\ Colin Barker, Nov 16 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Dec 03 2008
STATUS
approved