OFFSET
0,2
LINKS
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,1)
FORMULA
a(n) = 2*a(n-1) + a(n-2); a(0)=1, a(1)=8.
a(n) = ((7+sqrt(2))(1+sqrt(2))^n - (7-sqrt(2))(1-sqrt(2))^n)/2*sqrt(2).
G.f.: (1+6*x)/(1 - 2*x - x^2). - Philippe Deléham, Nov 03 2008
MAPLE
with(combinat): a:=n->6*fibonacci(n-1, 2)+fibonacci(n, 2): seq(a(n), n=1..26); # Zerinvary Lajos, Apr 04 2008
MATHEMATICA
a[n_]:=(MatrixPower[{{1, 2}, {1, 1}}, n].{{7}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
LinearRecurrence[{2, 1}, {1, 8}, 30] (* Harvey P. Dale, May 01 2013 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved