%I #19 Sep 08 2022 08:45:51
%S 1,1,1,4,1,1,9,9,1,1,16,29,16,1,1,31,81,67,25,1,1,64,241,256,129,36,1,
%T 1,129,729,1021,625,221,49,1,1,256,2189,4096,3121,1296,349,64,1,1,511,
%U 6561,16387,15625,7771,2401,519,81,1,1,1024,19681,65536,78129,46656,16801,4096,737,100,1,1
%N Array T(n, k) = k^(n-1) + (k-1)*cos(n*Pi/2), read by antidiagonals.
%C Row sums are {1, 2, 6, 20, 63, 206, 728, 2776, 11373, 49858, ...}.
%H G. C. Greubel, <a href="/A174006/b174006.txt">Antidiagonals n = 2..100, flattened</a>
%F T(n, k) = k^(n-1) + (k-1)*cos(n*Pi/2).
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 4, 1, 1;
%e 9, 9, 1, 1;
%e 16, 29, 16, 1, 1;
%e 31, 81, 67, 25, 1, 1;
%e 64, 241, 256, 129, 36, 1, 1;
%e 129, 729, 1021, 625, 221, 49, 1, 1;
%e 256, 2189, 4096, 3121, 1296, 349, 64, 1, 1;
%e 511, 6561, 16387, 15625, 7771, 2401, 519, 81, 1, 1;
%p T(n,k):= k^(n-1) + (k-1)*cos(n*Pi/2); seq(seq(T(n-k+1,k), k=2..n), n=2..12); # _G. C. Greubel_, Nov 28 2019
%t T[n_, k_]:= k^(n-1) + (k-1)*Cos[n*Pi/2]; Table[T[n-k+1, k], {n, 2, 12}, {k, 2, n}]//Flatten (* modified by _G. C. Greubel_, Nov 28 2019 *)
%o (PARI) T(n, k) = round(k^(n-1) + (k-1)*cos(n*Pi/2));
%o for(n=2, 12, for(k=2, n, print1(T(n-k+1,k), ", "))) \\ _G. C. Greubel_, Nov 28 2019
%o (Magma)
%o R:= RealField(10);
%o function T(n,k) return Round(k^(n-1) + (k-1)*Cos(n*Pi(R)/2)); end function;
%o [T(n-k+1,k): k in [2..n], n in [2..12]]; // _G. C. Greubel_, Nov 28 2019
%o (Sage)
%o @CachedFunction
%o def T(n, k): return k^(n-1) + (k-1)*cos(n*pi/2)
%o [[T(n-k+1, k) for k in (2..n)] for n in (2..12)] # _G. C. Greubel_, Nov 28 2019
%K nonn,tabl
%O 2,4
%A _Roger L. Bagula_, Mar 05 2010
%E Edited by _G. C. Greubel_, Dec 02 2019