OFFSET
0,1
COMMENTS
This is the Lucas sequence V(3,-4).
Inverse binomial transform of this sequence is A087451.
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..200
Wikipedia, Lucas sequence: Specific names.
Index entries for linear recurrences with constant coefficients, signature (3,4).
FORMULA
G.f.: (2-3*x)/((1+x)*(1-4*x)).
a(n) = 4^n+(-1)^n.
a(n) = [x^n] ( (1 + 3*x + sqrt(1 + 6*x + 25*x^2))/2 )^n for n >= 1. - Peter Bala, Jun 23 2015
a(n) = (2/4^n) * Sum_{k = 0..n} binomial(4*n+1, 4*k). - Peter Bala, Feb 06 2019
MATHEMATICA
RecurrenceTable[{a[n] == 3 a[n - 1] + 4 a[n - 2], a[0] == 2, a[1] == 3}, a[n], {n, 25}]
PROG
(Magma) [n le 1 select n+2 else 3*Self(n)+4*Self(n-1): n in [0..25]];
(Maxima) a[0]:2$ a[1]:3$ a[n]:=3*a[n-1]+4*a[n-2]$ makelist(a[n], n, 0, 25);
(PARI) Vec((2-3*x)/((1+x)*(1-4*x)) + O(x^30)) \\ Michel Marcus, Jun 26 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Jan 09 2013
STATUS
approved