A027657 Expansion of (1+4*x)/(1-34*x+x^2).

1, 38, 1291, 43856, 1489813, 50609786, 1719242911, 58403649188, 1984004829481, 67397760553166, 2289539853978163, 77776957274704376, 2642127007485970621, 89754541297248296738, 3049012277098956118471

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..650

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (34,-1).

Formula

a(n) = 34*a(n-1) - a(n-2) for n > 1; a(0)=1, a(1)=38. - Philippe Deléham, Nov 18 2008

a(n) = ChebyshevU(n, 17) + 4*ChebyshevU(n-1, 17). - G. C. Greubel, Aug 01 2022

Maple

f:= n -> orthopoly[U](n, 17)+4*orthopoly[U](n-1, 17):
f(0):= 1:
map(f, [$0..30]); # Robert Israel, Aug 02 2022

Mathematica

Transpose[NestList[{#[[2]], 34#[[2]]-#[[1]]}&, {1, 38}, 20]][[1]]  (* Harvey P. Dale, Mar 06 2011 *)
Table[ChebyshevU[n, 17] +4*ChebyshevU[n-1, 17], {n, 0, 30}] (* G. C. Greubel, Aug 01 2022 *)

Prog

(Magma) [n le 2 select (38)^(n-1) else 34*Self(n-1) -Self(n-2): n in [1..31]]; // G. C. Greubel, Aug 01 2022
(SageMath) [chebyshev_U(n, 17) +4*chebyshev_U(n-1, 17) for n in (0..30)] # G. C. Greubel, Aug 01 2022

Crossrefs

Cf. A029547.

Sequence in context: A268739 A239043 A137030 * A268885 A162858 A163221

Adjacent sequences: A027654 A027655 A027656 * A027658 A027659 A027660

Keyword

nonn

Author

N. J. A. Sloane

Status

approved