A349076 a(n) = U(n, 3*n), where U(n, x) is the Chebyshev polynomial of the second kind.

1, 6, 143, 5796, 330049, 24192090, 2168392031, 229755926568, 28093745899009, 3893604149949966, 603151411514453999, 103272803655639197580, 19367259480582106560193, 3947962681769909551857186, 869179946261864224288867775, 205535515565731164929726435280

Offset

0,2

Comments

In general, for k>=1, U(n, k*n) ~ 2^n * k^n * n^n.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..306

Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the Second Kind.

Wikipedia, Chebyshev polynomials.

Formula

a(n) = ((3*n + sqrt(9*n^2-1))^(n+1) - (3*n - sqrt(9*n^2-1))^(n+1)) / (2*sqrt(9*n^2-1)).

a(n) ~ 6^n * n^n.

Mathematica

Table[ChebyshevU[n, 3*n], {n, 0, 20}]

Prog

(PARI) a(n) = polchebyshev(n, 2, 3*n); \\ Michel Marcus, Nov 07 2021

Crossrefs

Cf. A323118, A349071, A349072, A349074, A349075.

Sequence in context: A277419 A349069 A111839 * A037049 A196811 A200457

Adjacent sequences: A349073 A349074 A349075 * A349077 A349078 A349079

Keyword

nonn

Author

Vaclav Kotesovec, Nov 07 2021

Status

approved