cp's OEIS Frontend

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).

%I A334178 #23 May 04 2021 02:11:16
%S A334178 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,
%T A334178 18,176,769,436,571,1,128,1,29,539,2911,8449,2089,2131,1,256,1,47,
%U A334178 1471,17753,48301,93127,10009,7953,1,512,1,76,4271,79808,603126,801701,1027207,47956,29681,1,1024
%N 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).
%F A334178 T(n,2*k) = A103997(n,k) for k > 0.
%e A334178 Square array begins:
%e A334178    1, 1,    1,     1,       1,        1,         1, ...
%e A334178    2, 1,    3,     4,       7,       11,        18, ...
%e A334178    4, 1,   11,    19,      71,      176,       539, ...
%e A334178    8, 1,   41,    91,     769,     2911,     17753, ...
%e A334178   16, 1,  153,   436,    8449,    48301,    603126, ...
%e A334178   32, 1,  571,  2089,   93127,   801701,  20721019, ...
%e A334178   64, 1, 2131, 10009, 1027207, 13307111, 714790675, ...
%t A334178 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 *)
%o A334178 (PARI) {T(n, k) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(k, 1, I*x/2)))}
%Y A334178 Rows 0..1 give A000012, A000032.
%Y A334178 Columns 0..15 give A000079, A000012, A001835(n+1), A004253(n+1), A334135, A003729, A334179, A028478, A334180, A028480, A334181, A028482, A334182, A028484, A334183, A028486.
%Y A334178 Cf. A103997.
%K A334178 nonn,tabl
%O A334178 0,3
%A A334178 _Seiichi Manyama_, Apr 17 2020