A341533 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} (4*sin((2*a-1)*Pi/(2*n))^2 + 4*sin((2*b-1)*Pi/k)^2) ).

2, 8, 2, 14, 36, 2, 36, 50, 200, 2, 82, 256, 224, 1156, 2, 200, 722, 2916, 1058, 6728, 2, 478, 2916, 9922, 38416, 5054, 39204, 2, 1156, 10082, 80000, 155682, 527076, 24200, 228488, 2, 2786, 38416, 401998, 2775556, 2540032, 7311616, 115934, 1331716, 2

Offset

1,1

Links

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

Example

Square array begins:
  2,     8,    14,      36,       82,        200, ...
  2,    36,    50,     256,      722,       2916, ...
  2,   200,   224,    2916,     9922,      80000, ...
  2,  1156,  1058,   38416,   155682,    2775556, ...
  2,  6728,  5054,  527076,  2540032,  105125000, ...
  2, 39204, 24200, 7311616, 41934482, 4115479104, ...

Prog

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

Crossrefs

Columns 1..7 give A007395, A341543, A231087, A341544, A231485, A341545, A230033.

Main diagonal gives A341535.

Cf. A340475.

Sequence in context: A222828 A222842 A098471 * A341741 A074723 A286455

Adjacent sequences: A341530 A341531 A341532 * A341534 A341535 A341536

Keyword

nonn,tabl

Author

Seiichi Manyama, Feb 13 2021

Status

approved