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A151617 Row sums of A153521. 2

%I

%S 2,22,242,2662,7986,45254,178354,854502,3670898,16741318,73862514,

%T 331879526,1476246706,6603168198,29445050162,131524950502,

%U 586945452786,2620665361094,11697730702834,52222780377702,233120598486578,1040691781127878,4645710145608114,20739029883622886,92580871368935026,413291071457721798

%N Row sums of A153521.

%H G. C. Greubel, <a href="/A151617/b151617.txt">Table of n, a(n) for n = 1..500</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,11).

%F From _G. C. Greubel_, Mar 04 2021: (Start)

%F 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.

%F G.f.: 2*x*(1 + 11*x + (11*x)^2*(1+9*x)/(1-2*x-11*x^2)).

%F G.f.: 2*x*(1 +9*x +88*x^2 +968*x^3)/(1-2*x-11*x^2).

%F 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.

%F 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)

%p m:= 40;

%p S:= series( x*(2 +18*x +176*x^2 +1936*x^3)/(1-2*x-11*x^2), x, m+1);

%p seq(coeff(S, x, j), j = 1..m); # _G. C. Greubel_, Mar 04 2021

%t LinearRecurrence[{2, 11}, {2, 22, 242, 2662}, 40] (* _G. C. Greubel_, Mar 04 2021 *)

%o (Sage)

%o def A151617_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( 2*x*(1 +9*x +88*x^2 +968*x^3)/(1-2*x-11*x^2) ).list()

%o a=A151617_list(41); a[1:] # _G. C. Greubel_, Mar 04 2021

%o (Magma)

%o R<x>:=PowerSeriesRing(Integers(), 41);

%o 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

%Y Cf. A153521.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, May 29 2009

%E Terms a(11) onward added by _G. C. Greubel_, Mar 04 2021

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Last modified July 26 22:49 EDT 2021. Contains 346300 sequences. (Running on oeis4.)