login
A250102
a(n) = 2*5^n - (1+2i)^(2n) - (1-2i)^(2n) where i = sqrt(-1).
2
0, 16, 64, 16, 2304, 5776, 7744, 309136, 451584, 2062096, 38837824, 27920656, 424030464, 4570300816, 1039933504, 74815378576, 501671890944, 2396689936, 11857885086784, 50863084730896, 8725926945024, 1727825132557456, 4673690093529664, 5056176437385616, 234290415599944704
OFFSET
0,2
LINKS
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.
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
Equals 16*A094423.
Sequence in context: A333663 A155985 A211222 * A322032 A090567 A255660
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 15 2014
STATUS
approved