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A106851
Expansion of (-3*x^3 - 7*x^2 + 2*x)/((1-4*x-x^2)*(1-4*x+x^2)).
0
0, 2, 9, 37, 152, 626, 2585, 10701, 44400, 184610, 769065, 3209461, 13415048, 56153618, 235357241, 987609501, 4148575200, 17443003202, 73402179657, 309116995525, 1302649664888, 5492768393906, 23173154692697, 97810060234605
OFFSET
0,2
FORMULA
G.f.: (-3*x^3 - 7*x^2 + 2*x)/((1-4*x-x^2)*(1-4*x+x^2)).
a(n) = (1/2) * [A001834(n-1) + Fibonacci(3n+1) ]. - Ralf Stephan, Nov 18 2010
a(0)=0, a(1)=2, a(2)=9, a(3)=37, a(n)=8*a(n-1)-16*a(n-2)+a(n-4) [Harvey P. Dale, Aug 05 2011]
MATHEMATICA
CoefficientList[Series[(-3 x^3-7x^2+2x)/((1-4x-x^2)(1-4x+x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -16, 0, 1}, {0, 2, 9, 37}, 31] (* Harvey P. Dale, Aug 05 2011 *)
CROSSREFS
Sequence in context: A037553 A178875 A012493 * A129169 A162548 A150983
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, May 30 2005
EXTENSIONS
Edited by N. J. A. Sloane, Apr 09 2007
New name from Joerg Arndt, Dec 26 2022
STATUS
approved