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A048877
a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=8.
2
1, 8, 33, 140, 593, 2512, 10641, 45076, 190945, 808856, 3426369, 14514332, 61483697, 260449120, 1103280177, 4673569828, 19797559489, 83863807784, 355252790625, 1504874970284, 6374752671761
OFFSET
0,2
COMMENTS
Generalized Pellian with second term of 8.
FORMULA
a(n) = ((6+sqrt(5))*(2+sqrt(5))^n - (6-sqrt(5))*(2-sqrt(5))^n )/(2*sqrt(5)).
G.f.: (1+4*x)/(1-4*x-x^2). - Philippe Deléham, Nov 03 2008
a(n)=4*a(n-1) + a(n-2); a(0)=1, a(1)=8.
MAPLE
with(combinat): a:=n->4*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008
MATHEMATICA
CoefficientList[Series[(1+4x)/(1-4x-x^2), {x, 0, 20}], x] (* Harvey P. Dale, Mar 30 2011 *)
LinearRecurrence[{4, 1}, {1, 8}, 30] (* Harvey P. Dale, Nov 03 2013 *)
PROG
(Haskell)
a048877 n = a048877_list !! n
a048877_list = 1 : 8 : zipWith (+) a048877_list (map (* 4) $ tail a048877_list)
-- Reinhard Zumkeller, May 01 2013
CROSSREFS
KEYWORD
easy,nonn
STATUS
approved