A349074 a(n) = U(3*n, n), where U(n, x) is the Chebyshev polynomial of the second kind.

1, 4, 2911, 7997214, 57641556673, 867583274883920, 23630375698358890319, 1056918444955456528983706, 72383076947075470731692782081, 7200266529428094485775774835670652, 998383804974887102441600687728515247999, 186701261436825568741051032736345268517903734

Offset: 0

Author

Vaclav Kotesovec, Nov 07 2021

Keywords

• nonn

Comments

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..136
• Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the Second Kind.
• Wikipedia, Chebyshev polynomials.

Crossrefs

Cf. A323118, A349070, A349073, A349076.

Programs

Mathematica

Table[ChebyshevU[3*n, n], {n, 0, 13}]

PARI

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

Python

from sympy import chebyshevu
def A349074(n): return chebyshevu(3*n,n) # Chai Wah Wu, Nov 08 2023

Formula

For n>1, a(n) = ((n + sqrt(n^2-1))^(3*n+1) - (n - sqrt(n^2-1))^(3*n+1)) / (2*sqrt(n^2-1)).

a(n) ~ 2^(3*n) * n^(3*n).