A362357 Bisection of Chebyshev {S(n, 5)}_{n>=0}; the even part.

1, 24, 551, 12649, 290376, 6665999, 153027601, 3512968824, 80645255351, 1851327904249, 42499896542376, 975646292570399, 22397364832576801, 514163744856696024, 11803368766871431751, 270963317893186234249

Offset

0,2

Comments

The odd part of this bisection is given by 5*A097778(n), for n >= 0.

Links

Table of n, a(n) for n=0..15.

Index entries for sequences related to Chebyshev polynomials.`

Index entries for linear recurrences with constant coefficients, signature (23,-1).

Formula

a(n) = S(2*n, 5) = S(n, 23) + S(n-1, 23), with the Chebyshev S polynomials (see A049310), S(-1, x) = 0, S(n, 5) = A004254(n+1) and S(n, 23) = A097778(n).

O.g.f.: (1 + x)/(1 - 23*x + x^2).

a(n) = 23*a(n-1) - a(n-2), for n >= 0, with a(-1) = -1 and a(-2) = -24.

Mathematica

Table[ChebyshevU[2*n, 5/2], {n, 0, 20}] (* Vaclav Kotesovec, May 27 2023 *)

Prog

(PARI) a(n) = polchebyshev(2*n, 2, 5/2); \\ Michel Marcus, May 27 2023

Crossrefs

Cf. A004254, A049310, A097778.

Sequence in context: A235118 A223099 A187671 * A162810 A010561 A334673

Adjacent sequences: A362354 A362355 A362356 * A362358 A362359 A362360

Keyword

nonn,easy

Author

Wolfdieter Lang, Apr 26 2023

Status

approved