cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A340427 Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) = 4^(2*(n-1)*(k-1)) * Product_{a=1..n-1} Product_{b=1..k-1} (1 - sin(a*Pi/(2*n))^2 * sin(b*Pi/(2*k))^2).

Original entry on oeis.org

1, 1, 1, 1, 12, 1, 1, 140, 140, 1, 1, 1632, 17745, 1632, 1, 1, 19024, 2227120, 2227120, 19024, 1, 1, 221760, 279215849, 2958176256, 279215849, 221760, 1, 1, 2585024, 35001302700, 3909096873216, 3909096873216, 35001302700, 2585024, 1
Offset: 1

Views

Author

Seiichi Manyama, Jan 07 2021

Keywords

Examples

			Square array begins:
  1,     1,         1,             1,                 1, ...
  1,    12,       140,          1632,             19024, ...
  1,   140,     17745,       2227120,         279215849, ...
  1,  1632,   2227120,    2958176256,     3909096873216, ...
  1, 19024, 279215849, 3909096873216, 54090331699622625, ...
		

Crossrefs

Main diagonal gives A340166.

Programs

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

Formula

T(n,k) = T(k,n).
T(n,k) = 4^(2*(n-1)*(k-1)) * Product_{a=1..n-1} Product_{b=1..k-1} (1 - cos(a*Pi/(2*n))^2 * cos(b*Pi/(2*k))^2).
T(n,k) = 4^(2*(n-1)*(k-1)) * Product_{a=1..n-1} Product_{b=1..k-1} (1 - sin(a*Pi/(2*n))^2 * cos(b*Pi/(2*k))^2).

A340428 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = 4^(2*n*k) * Product_{a=1..n} Product_{b=1..k} (1 - sin(a*Pi/(2*n+1))^2 * sin(b*Pi/(2*k+1))^2).

Original entry on oeis.org

1, 1, 1, 1, 7, 1, 1, 61, 61, 1, 1, 547, 4961, 547, 1, 1, 4921, 432461, 432461, 4921, 1, 1, 44287, 38484961, 371647151, 38484961, 44287, 1, 1, 398581, 3445022461, 330435708793, 330435708793, 3445022461, 398581, 1
Offset: 0

Views

Author

Seiichi Manyama, Jan 07 2021

Keywords

Examples

			Square array begins:
  1,    1,        1,            1,                1, ...
  1,    7,       61,          547,             4921, ...
  1,   61,     4961,       432461,         38484961, ...
  1,  547,   432461,    371647151,     330435708793, ...
  1, 4921, 38484961, 330435708793, 2952717950351617, ...
		

Crossrefs

Main diagonal gives A340292.

Programs

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

Formula

T(n,k) = T(k,n).

A340430 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = 4^(2*n*k) * Product_{a=1..n} Product_{b=1..k} (1 - cos(a*Pi/(2*n+1))^2 * cos(b*Pi/(2*k+1))^2).

Original entry on oeis.org

1, 1, 1, 1, 15, 1, 1, 209, 209, 1, 1, 2911, 32625, 2911, 1, 1, 40545, 5015009, 5015009, 40545, 1, 1, 564719, 770100001, 8238791743, 770100001, 564719, 1, 1, 7865521, 118247646001, 13441754883649, 13441754883649, 118247646001, 7865521, 1
Offset: 0

Views

Author

Seiichi Manyama, Jan 07 2021

Keywords

Examples

			Square array begins:
  1,     1,         1,              1,                  1, ...
  1,    15,       209,           2911,              40545, ...
  1,   209,     32625,        5015009,          770100001, ...
  1,  2911,   5015009,     8238791743,     13441754883649, ...
  1, 40545, 770100001, 13441754883649, 230629380093001665, ...
		

Crossrefs

Main diagonal gives A340291.

Programs

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

Formula

T(n,k) = T(k,n).
Showing 1-3 of 3 results.