OFFSET
0,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..1430
Ira M. Gessel, Rational Functions With Nonnegative Integer Coefficients, slides, 50th Séminaire Lotharingien de Combinatoire, 2003.
Igor Pak, Complexity problems in enumerative combinatorics, arXiv:1803.06636 [math.CO], 2018.
Index entries for linear recurrences with constant coefficients, signature (-1,5,125).
FORMULA
From Colin Barker, Feb 20 2019: (Start)
G.f.: 16*x*(1 + 5*x) / ((1 - 5*x)*(1 + 6*x + 25*x^2)).
a(n) = -a(n-1) + 5*a(n-2) + 125*a(n-3) for n>2.
(End)
MATHEMATICA
Array[2*5^# - (1 + 2 I)^(2 #) - (1 - 2 I)^(2 #) &, 25, 0] (* Michael De Vlieger, Jun 19 2018 *)
LinearRecurrence[{-1, 5, 125}, {0, 16, 64}, 30] (* Harvey P. Dale, May 26 2020 *)
PROG
(PARI) a(n) = 2*5^n - (1+2*I)^(2*n) - (1-2*I)^(2*n) \\ Michel Marcus, Aug 28 2015
(PARI) concat(0, Vec(16*x*(1 + 5*x) / ((1 - 5*x)*(1 + 6*x + 25*x^2)) + O(x^30))) \\ Colin Barker, Feb 20 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 15 2014
STATUS
approved