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

Author

Wolfdieter Lang, Apr 26 2023

Keywords

• nonn
• easy

Comments

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

Links

• Index entries for sequences related to Chebyshev polynomials.`
• Index entries for linear recurrences with constant coefficients, signature (23,-1).

Crossrefs

Cf. A004254, A049310, A097778.

Programs

Mathematica

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

PARI

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

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.