login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
OFFSET
1,1
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
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