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A027657
Expansion of (1+4*x)/(1-34*x+x^2).
1
1, 38, 1291, 43856, 1489813, 50609786, 1719242911, 58403649188, 1984004829481, 67397760553166, 2289539853978163, 77776957274704376, 2642127007485970621, 89754541297248296738, 3049012277098956118471
OFFSET
0,2
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
KEYWORD
nonn
STATUS
approved