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A122006 Expansion of x^2*(1-x)/((1-3*x)*(1-3*x^2)). 3
0, 1, 2, 9, 24, 81, 234, 729, 2160, 6561, 19602, 59049, 176904, 531441, 1593594, 4782969, 14346720, 43046721, 129133602, 387420489, 1162241784, 3486784401, 10460294154, 31381059609, 94143001680, 282429536481, 847288078002, 2541865828329, 7625595890664 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

The sequence can be created by multiplying the n-th power of the matrix [[0,1,2],[1,2,0],[2,0,1]], multiplying from the right with the vector [1,0,0] and taking the middle element of the resulting vector.

REFERENCES

Alain M. Robert, "Linear Algebra, Examples and Applications", 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

a(n) = 3*a(n-1) + 3*a(n-2) - 9*a(n-3). - Philippe Deléham, Mar 09 2009

From Colin Barker, Sep 23 2016: (Start)

a(n) = 3^(n-2) for n even.

a(n) = 3^(n-2)-3^((n-3)/2) for n 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][[2]], {n, 1, 50}]

PROG

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

CROSSREFS

Cf. A007179.

Sequence in context: A275260 A248436 A222667 * A200086 A143561 A027302

Adjacent sequences:  A122003 A122004 A122005 * A122007 A122008 A122009

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified February 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)