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A212335
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Expansion of 1/(1-22*x+22*x^2-x^3).
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2
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1, 22, 462, 9681, 202840, 4249960, 89046321, 1865722782, 39091132102, 819048051361, 17160917946480, 359560228824720, 7533603887372641, 157846121406000742, 3307234945638642942, 69294087737005501041, 1451868607531476878920
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: 1/((1-x)*(1-21*x+x^2)).
a(n) = (((230-11*sqrt(437))*(21-sqrt(437))^n+(230+11*sqrt(437))*(21+sqrt(437))^n)/2^n-23)/437.
a(n) = a(-n-3) = 23*a(n-1)-23*a(n-2)+a(n-3).
a(n)*a(n+2) = a(n+1)*(a(n+1)-1).
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MAPLE
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a:= n-> (<<0|1|0>, <0|0|1>, <1|-22|22>>^n. <<1, 22, 462>>)[1, 1]:
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MATHEMATICA
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CoefficientList[Series[1/(1 - 22 x + 22 x^2 - x^3), {x, 0, 16}], x]
LinearRecurrence[{22, -22, 1}, {1, 22, 462}, 20] (* Harvey P. Dale, Nov 04 2017 *)
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PROG
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(PARI) Vec(1/(1-22*x+22*x^2-x^3)+O(x^17))
(Maxima) makelist(coeff(taylor(1/(1-22*x+22*x^2-x^3), x, 0, n), x, n), n, 0, 16);
(Magma) m:=17; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-22*x+22*x^2-x^3)));
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CROSSREFS
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Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3).
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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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