A106851 Expansion of (-3*x^3 - 7*x^2 + 2*x)/((1-4*x-x^2)*(1-4*x+x^2)).
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
Links
- Index entries for linear recurrences with constant coefficients, signature (8, -16, 0, 1).
Programs
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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 *)
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]
Extensions
Edited by N. J. A. Sloane, Apr 09 2007
New name from Joerg Arndt, Dec 26 2022