A174443 Generating function x/(1+4*x-8*x^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

Nathaniel Johnston, Table of n, a(n) for n = 0..500

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

Adjacent sequences: A174440 A174441 A174442 * A174444 A174445 A174446

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