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A122584 Expansion of x*(1+x)*(2*x-1) / ( -1+2*x+x^2-2*x^3+x^4 ). 3
1, 1, 1, 1, 2, 4, 9, 19, 41, 87, 186, 396, 845, 1801, 3841, 8189, 17462, 37232, 79389, 169275, 360937, 769603, 1640982, 3498968, 7460649, 15907905, 33919505, 72324585, 154213514, 328820508, 701124865, 1494967795, 3187632953 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

REFERENCES

A. Messiah, Quantum mechanics, vol. 2, p. 608-609, eq.(XIV.57), North Holland, 1969.

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..3000

Miklos Bona, Rebecca Smith, Pattern avoidance in permutations and their squares, arXiv:1901.00026 [math.CO], 2018. See p. 6.

Index entries for linear recurrences with constant coefficients, signature (2,1,-2,1).

MAPLE

seq(coeff(series((x*(1+x)*(2*x-1))/(x^4-2*x^3+x^2+2*x-1), x, n+1), x, n), n = 1 .. 40); # Muniru A Asiru, Jan 03 2019

MATHEMATICA

M = {{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, -2, 0, 1, 0, 2, 0}}; v[1] = Table[1, {n, 1, 8}]; v[n_] := v[n] = M.v[n - 1]; a = Table[v[2*n][[1]], {n, 1, 50}]

PROG

(PARI) Vec(x*(1+x)*(2*x-1)/(-1+2*x+x^2-2*x^3+x^4)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

CROSSREFS

Sequence in context: A052908 A036616 A136298 * A184936 A330489 A299106

Adjacent sequences:  A122581 A122582 A122583 * A122585 A122586 A122587

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Sep 19 2006

STATUS

approved

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Last modified September 21 06:18 EDT 2021. Contains 347596 sequences. (Running on oeis4.)