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A077937
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Expansion of 1/(1-2*x-2*x^2+2*x^3).
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9
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1, 2, 6, 14, 36, 88, 220, 544, 1352, 3352, 8320, 20640, 51216, 127072, 315296, 782304, 1941056, 4816128, 11949760, 29649664, 73566592, 182532992, 452899840, 1123732480, 2788198656, 6918062592, 17165057536, 42589842944, 105673675776, 262196922368
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OFFSET
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0,2
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COMMENTS
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Form the graph with matrix A = [1,1,1,1; 1,0,0,0; 1,0,0,0; 1,0,0,1]. Then the sequence 0, 1, 2, 6, ... counts walks of length n between the degree 5 vertex and the degree 3 vertex. - Paul Barry, Oct 02 2004
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LINKS
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FORMULA
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a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) with a(0) = 1, a(1) = 2, and a(3) = 8. - G. C. Greubel, May 02 2022
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MATHEMATICA
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CoefficientList[Series[1/(1-2*x-2*x^2+2*x^3), {x, 0, 40}], x] (* Harvey P. Dale, Dec 05 2018 *)
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PROG
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(Magma) [n le 3 select Factorial(n) else 2*(Self(n-1) +Self(n-2) -Self(n-3)): n in [1..51]]; # G. C. Greubel, May 02 2022
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-2*x-2*x^2+2*x^3) ).list()
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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