A341738 Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) = sqrt( Product_{a=1..n} Product_{b=1..k-1} (4*sin((2*a-1)*Pi/(2*n))^2 + 4*sin(2*b*Pi/k)^2) ).

1, 2, 1, 7, 2, 1, 16, 25, 2, 1, 41, 72, 112, 2, 1, 98, 361, 400, 529, 2, 1, 239, 1250, 4961, 2312, 2527, 2, 1, 576, 5041, 25088, 77841, 13456, 12100, 2, 1, 1393, 18432, 200999, 559682, 1270016, 78408, 57967, 2, 1

Offset

1,2

Links

Table of n, a(n) for n=1..45.

Formula

If k is odd, T(n,k) = A341533(n,k)/2.

Example

Square array begins:
  1, 2,     7,    16,       41,        98, ...
  1, 2,    25,    72,      361,      1250, ...
  1, 2,   112,   400,     4961,     25088, ...
  1, 2,   529,  2312,    77841,    559682, ...
  1, 2,  2527, 13456,  1270016,  12771458, ...
  1, 2, 12100, 78408, 20967241, 292820000, ...

Prog

(PARI) default(realprecision, 120);
T(n, k) = round(sqrt(prod(a=1, n, prod(b=1, k-1, 4*sin((2*a-1)*Pi/(2*n))^2+4*sin(2*b*Pi/k)^2))));

Crossrefs

Main diagonal gives A341782.

Cf. A341533, A341739, A341741.

Sequence in context: A335405 A369924 A347800 * A128747 A205945 A124392

Adjacent sequences: A341735 A341736 A341737 * A341739 A341740 A341741

Keyword

nonn,tabl

Author

Seiichi Manyama, Feb 18 2021

Status

approved