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A174443
Generating function x/(1+4*x-8*x^2).
2
0, 1, -4, 24, -128, 704, -3840, 20992, -114688, 626688, -3424256, 18710528, -102236160, 558628864, -3052404736, 16678649856, -91133837312, 497964548096, -2720928890880, 14867431948288, -81237158920192, 443888091267072, -2425449636429824, 13252903275855872
OFFSET
0,3
COMMENTS
Binet form: with a = 4/(1 + sqrt(3)); b = 4/(1 - sqrt(3)); we have a(n)=(a^n - b^n)/(a - b).
Alternative expressions for the roots are -2 +- 2*sqrt(3).
Limiting ratio a(n+1)/a(n) is:-5.464101615137755== -2-2*sqrt(3).
LINKS
FORMULA
a(0)=0, a(1)=1, a(n) = -4a(n-1) + 8a(n-2).
a(0)=0, a(n) = (-2)^(n-1)*A002605(n).
MATHEMATICA
a = 4/(1 + Sqrt[3]); b = 4/(1 - Sqrt[3]);
f[n_] = (a^n - b^n)/(a - b);
Table[FullSimplify[f[n]], {n, 0, 30}]
CROSSREFS
Cf. A180222 (unsigned version of this sequence).
Sequence in context: A024049 A103455 A289715 * A180222 A192070 A048180
KEYWORD
sign,easy
AUTHOR
Roger L. Bagula, Nov 28 2010
EXTENSIONS
Correction of the Mathematica code and better name by Joerg Arndt.
Formulae and edited by Ralf Stephan, Nov 27 2010
STATUS
approved