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A298271
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Expansion of x/((1 - x)*(1 - 322*x + x^2)).
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3
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0, 1, 323, 104006, 33489610, 10783550415, 3472269744021, 1118060074024348, 360011871566096036, 115922704584208899245, 37326750864243699460855, 12019097855581887017496066, 3870112182746503375934272398, 1246164103746518505163818216091
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: x/((1 - x)*(1 - 322*x + x^2)).
a(n) = a(-n-1) = 323*a(n-1) - 323*a(n-2) + a(n-3).
a(n) = (1/5760)*((2 + sqrt(5))^(4*n+2) + (2 + sqrt(5))^-(4*n+2) - 18).
a(n) - a(n-1) = (1/144)*Fibonacci(12*n).
a(n) - a(n-2) = (1/8)*Fibonacci(12*n-6).
a(n)*a(n-2) = a(n-1)*(a(n-1) - 1).
Sum_{j>1} 1/a(j) = 161 - 72*sqrt(5) = A094214^12.
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MATHEMATICA
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CoefficientList[x/((1 - x) (1 - 322 x + x^2)) + O[x]^20, x]
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PROG
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(Sage)
gf = x/((1-x)*(1-322*x+x^2))
print(taylor(gf, x, 0, 20).list())
(Maxima) makelist(coeff(taylor(x/((1-x)*(1-322*x+x^2)), x, 0, n), x, n), n, 0, 20);
(PARI) concat(0, Vec(x / ((1 - x)*(1 - 322*x + x^2)) + O(x^15))) \\ Colin Barker, Jan 19 2018
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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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