login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

A334178
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{k}(i*x/2))), where T_n(x) is a Chebyshev polynomial of the first kind, U_n(x) is a Chebyshev polynomial of the second kind and i = sqrt(-1).
6
1, 1, 2, 1, 1, 4, 1, 3, 1, 8, 1, 4, 11, 1, 16, 1, 7, 19, 41, 1, 32, 1, 11, 71, 91, 153, 1, 64, 1, 18, 176, 769, 436, 571, 1, 128, 1, 29, 539, 2911, 8449, 2089, 2131, 1, 256, 1, 47, 1471, 17753, 48301, 93127, 10009, 7953, 1, 512, 1, 76, 4271, 79808, 603126, 801701, 1027207, 47956, 29681, 1, 1024
OFFSET
0,3
FORMULA
T(n,2*k) = A103997(n,k) for k > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
2, 1, 3, 4, 7, 11, 18, ...
4, 1, 11, 19, 71, 176, 539, ...
8, 1, 41, 91, 769, 2911, 17753, ...
16, 1, 153, 436, 8449, 48301, 603126, ...
32, 1, 571, 2089, 93127, 801701, 20721019, ...
64, 1, 2131, 10009, 1027207, 13307111, 714790675, ...
MATHEMATICA
T[n_, k_] := 2^n * Sqrt[Resultant[ChebyshevU[2*n, x/2], ChebyshevT[k, I*x/2], x]]; Table[T[k, n - k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, May 04 2021 *)
PROG
(PARI) {T(n, k) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(k, 1, I*x/2)))}
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Apr 17 2020
STATUS
approved