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

1,2

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).

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)

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}]

Prog

(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

Crossrefs

Sequence in context: A355871 A164961 A362192 * A365643 A137782 A131384

Adjacent sequences: A122004 A122005 A122006 * A122008 A122009 A122010

Keyword

nonn,easy

Author

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

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

Status

approved