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A151617 Row sums of A153521. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (2,11).

FORMULA

From G. C. Greubel, Mar 04 2021: (Start)

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)

MAPLE

m:= 40;

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

seq(coeff(S, x, j), j = 1..m); # G. C. Greubel, Mar 04 2021

MATHEMATICA

LinearRecurrence[{2, 11}, {2, 22, 242, 2662}, 40] (* G. C. Greubel, Mar 04 2021 *)

PROG

(Sage)

def A151617_list(prec):

    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()

a=A151617_list(41); a[1:] # G. C. Greubel, Mar 04 2021

(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

CROSSREFS

Cf. A153521.

Sequence in context: A089182 A138140 A322283 * A334603 A342232 A082777

Adjacent sequences:  A151614 A151615 A151616 * A151618 A151619 A151620

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 29 2009

EXTENSIONS

Terms a(11) onward added by G. C. Greubel, Mar 04 2021

STATUS

approved

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Last modified June 18 06:58 EDT 2021. Contains 345098 sequences. (Running on oeis4.)