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A072335 Expansion of 1/((1-x^2)*(1-4*x+x^2)). 5
1, 4, 16, 60, 225, 840, 3136, 11704, 43681, 163020, 608400, 2270580, 8473921, 31625104, 118026496, 440480880, 1643897025, 6135107220, 22896531856, 85451020204, 318907548961, 1190179175640, 4441809153600, 16577057438760, 61866420601441, 230888624967004 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
N. J. A. Sloane, Transforms
FORMULA
a(n) = (1/12)*((7-4*sqrt(3))*(2-sqrt(3))^n+(7+4*sqrt(3))*(2+sqrt(3))^n-3+(-1)^n). Recurrence: a(n) = 4*a(n-1)-4*a(n-3)+a(n-4).
a(n)=sum{k=0..floor(n/2), U(n-2k, 2)} - Paul Barry, Nov 15 2003
The g.f. can also be written as 1/(1-4*x+4*x^3-x^4), which relates this sequence to the family of sequences described in A225682.
MATHEMATICA
CoefficientList[Series[1/((1-x^2)*(1-4x+x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[{4, 0, -4, 1}, {1, 4, 16, 60}, 30] (* Harvey P. Dale, Aug 22 2015 *)
PROG
(PARI) Vec(1/((1-x^2)*(1-4*x+x^2))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
EULER transform of A072279 (with its initial 1 omitted).
A001353(n)^2 is a bisection of a(n).
Cf. A225682.
Sequence in context: A269673 A231896 A128650 * A081161 A032106 A269462
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 15 2002
STATUS
approved

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Last modified April 21 19:32 EDT 2024. Contains 371885 sequences. (Running on oeis4.)