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