82224

Appears in sequences

• a(n) is the number of pairs of integer quadruples (b_1, b_2, b_3, b_4) and (c_1, c_2, c_3, c_4) satisfying 1 <= b_1 < b_2 < b_3 < b_4 < n, 1 <= c_1 < c_2 < c_3 < c_4 < n, b_i != c_j for all i,j = 1,2,3,4 and Product_{i=1..4} cos(2*Pi*b_i/n) = Product_{i=1..4} cos(2*Pi*c_i/n).at n=48A063780
• Number of slanted nX8 (i=1..n)X(j=i..8+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, and 4 in the lower right corner.at n=1A165377
• Number of slanted 3 X n (i=1..3) X (j=i..n+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, and 4 in the lower right corner.at n=6A165386
• Number of (n+1)X8 0..1 arrays with the number of rightwards and downwards edge increases in each 2X2 subblock differing from the number in all its horizontal and vertical neighbors.at n=14A205071
• a(n) where a(n) * a(n-5) * a(n-10) = a(n-1) * a(n-6) * a(n-8) + a(n-2) * a(n-4) * a(n-9), with a(1) = ... = a(10) = 1.at n=24A205303
• a(n) = n! * Sum_{k=1..n} A008836(k)/k.at n=8A281510
• a(n) = n! * Sum_{k=0..n} (2*k)! / (k!)^3.at n=7A349513