A151617 Row sums of A153521.

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

Offset: 1

Author

N. J. A. Sloane, May 29 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (2,11).

Crossrefs

Cf. A153521.

Programs

Magma

R:=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

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 *)

Sage

def A151617_list(prec):
    P. = 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

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)

Extensions

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