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A095897
Expansion of x*(1+4*x-4*x^2)/((1+2*x)*(1-6*x)*(1-8*x^2)).
5
1, 8, 48, 320, 1888, 11648, 69504, 419840, 2515456, 15116288, 90667008, 544194560, 3264913408, 19591036928, 117544157184, 705277460480, 4231648116736, 25389989101568, 152339800915968, 914039609753600, 5484236586876928
OFFSET
1,2
FORMULA
a(n) = 4*a(n-1) + 20*a(n-2) - 32*a(n-3) - 96*a(n-4) for n > 4.
From Bruno Berselli, Aug 04 2011: (Start)
G.f.: x*(1+4*x-4*x^2)/((1+2*x)*(1-6*x)*(1-8*x^2)).
a(n) = 2^(n-2)*(3^n-1+((-1)^n-1)*(sqrt(2)^(n-1)-1)).
a(2k+1) = 2^(2k-1)*(3*9^k-2*2^k+1), a(2k) = 4^(k-1)*(9^k-1). (End)
MATHEMATICA
LinearRecurrence[{4, 20, -32, -96}, {1, 8, 48, 320}, 30] (* Harvey P. Dale, Jun 11 2011 *)
PROG
(Magma) [Floor(2^(n-2)*(3^n-1+((-1)^n-1)*(Sqrt(2)^(n-1)-1))): n in [1..30]]; // Vincenzo Librandi, Aug 05 2011
CROSSREFS
Sequence in context: A037690 A180031 A203799 * A220251 A025013 A215706
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jun 11 2004
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Jun 16 2004
Meaningful name from Joerg Arndt, Dec 26 2022
STATUS
approved