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2, 22, 242, 2662, 7986, 45254, 178354, 854502, 3670898, 16741318, 73862514, 331879526, 1476246706, 6603168198, 29445050162, 131524950502, 586945452786, 2620665361094, 11697730702834, 52222780377702, 233120598486578, 1040691781127878, 4645710145608114, 20739029883622886, 92580871368935026, 413291071457721798
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = 2*a(n-1) + 11*a(n-2), for n>4, with a(1)=2, a(2)=22, a(3)=242, a(4)=2662.
G.f.: 2*x*(1 + 11*x + (11*x)^2*(1+9*x)/(1-2*x-11*x^2)).
G.f.: 2*x*(1 +9*x +88*x^2 +968*x^3)/(1-2*x-11*x^2).
a(n) = 2*a(n-1) + prime(j)*a(n-2), for n > 4, with a(1) = 2, a(2) = 2*prime(j), a(3) = 2*prime(j)^2, a(4) = 2*prime(j)^3 for j = 5.
a(n) = 2*(prime(j)-3)*[n=1] -2*prime(j)*(prime(j)-3)*[n=2] +2*prime(j)^2*(i*sqrt(prime(j)))^(n-3)*(ChebyshevU(n-3, -i/Sqrt(prime(j))) -((prime(j) -2)*i/sqrt(prime(j)))*ChebyshevU(n-4, -i/sqrt(prime(j)))) for j = 5. (End)
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MAPLE
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m:= 40;
S:= series( x*(2 +18*x +176*x^2 +1936*x^3)/(1-2*x-11*x^2), x, m+1);
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MATHEMATICA
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LinearRecurrence[{2, 11}, {2, 22, 242, 2662}, 40] (* G. C. Greubel, Mar 04 2021 *)
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PROG
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(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 2*x*(1 +9*x +88*x^2 +968*x^3)/(1-2*x-11*x^2) ).list()
(Magma)
R<x>:=PowerSeriesRing(Integers(), 41);
Coefficients(R!( 2*x*(1 +9*x +88*x^2 +968*x^3)/(1-2*x-11*x^2) )); // G. C. Greubel, Mar 04 2021
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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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EXTENSIONS
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STATUS
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approved
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