A341576 a(n) = Sum_{k=0..n} U_k((n-k)/2) where U_n(x) is a Chebyshev polynomial of the 2nd kind.

1, 1, 1, 3, 7, 16, 46, 149, 520, 1977, 8136, 35878, 168501, 838945, 4409957, 24385913, 141412615, 857611640, 5426144190, 35739397739, 244573978100, 1735854397529, 12757309001220, 96941738970956, 760649367654461, 6155205917196409, 51308394497243469

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Index entries for sequences related to Chebyshev polynomials.

Mathematica

a[n_] := Sum[ChebyshevU[k, (n - k)/2], {k, 0, n}]; Array[a, 27, 0] (* Amiram Eldar, Mar 08 2021 *)

Prog

(PARI) a(n) = sum(k=0, n, polchebyshev(k, 2, (n-k)/2));
(Python)
from fractions import Fraction
from sympy import chebyshevu
def A341576(n): return sum(chebyshevu(k, Fraction(n-k, 2)) for k in range(n+1)) # Chai Wah Wu, Nov 08 2023

Crossrefs

Cf. A101125, A323613.

Sequence in context: A360782 A351821 A005312 * A143817 A297210 A000963

Adjacent sequences: A341573 A341574 A341575 * A341577 A341578 A341579

Keyword

nonn

Author

Seiichi Manyama, Mar 08 2021

Status

approved