A122007 Expansion of 2*x^2*(1-2*x) / ((3*x-1)*(3*x^2-1)).

0, 2, 2, 12, 24, 90, 234, 756, 2160, 6642, 19602, 59292, 176904, 532170, 1593594, 4785156, 14346720, 43053282, 129133602, 387440172, 1162241784, 3486843450, 10460294154, 31381236756, 94143001680, 282430067922, 847288078002, 2541867422652, 7625595890664

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Sep 11 2006

Keywords

• nonn
• easy

References

• "Linear Algebra, Examples and Applications" by Alain M. Robert, World Scientific, 2005, p. 58.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,3,-9).

Programs

Mathematica

M = {{0, 1, 2}, {1, 2, 0}, {2, 0, 1}} v[1] = {1, 0, 0} v[n_] := v[n] = M.v[n - 1] a1 = Table[v[n][[3]], {n, 1, 50}]

PARI

concat(0, Vec(2*x^2*(1-2*x)/((3*x-1)*(3*x^2-1)) + O(x^40))) \\ Colin Barker, Sep 23 2016

Formula

Limit a(n+1)/a(n)= 3 as n-> infinity.

a(n)= 3*a(n-1) +3*a(n-2) -9*a(n-3) = 3^(n-2) + (-1)^n*A108411(n-2), n>=2.

From Colin Barker, Sep 23 2016: (Start)

a(n) = 3^(n/2-1)+3^(n-2) for n>1 and even.

a(n) = 3^(n-2)-3^((n-3)/2) for n>1 and odd.

(End)

Extensions

Definition replaced with generating function by the Assoc. Eds. of the OEIS, Mar 27 2010

A-number in formula corrected - R. J. Mathar, Mar 30 2010