OFFSET
2,1
LINKS
D. Edelman and A. Edelman, Solution 1877: Disconnecting a permutation matrix, Math. Mag. 85 (2012) 297-298.
FORMULA
a(n) = 4 Sum_{i=1..n-2} i! - 2(n-2) Sum_{i=0..n-4} i! + 2 Sum_{i=1..n-3} i! + 2.
Conjecture: 2*a(n) + 2*(-n-1)*a(n-1) + (6*n-11)*a(n-2) + (-5*n+14)*a(n-3) + 3*a(n-4) + (n-6)*a(n-5) = 0. - R. J. Mathar, Nov 30 2012
Recurrence (for n>4): (2*n^2 - 16*n + 31)*a(n) = (2*n^3 - 16*n^2 + 33*n - 6)*a(n-1) - (2*n-7)*(2*n^2 - 12*n + 15)*a(n-2) + (n-4)*(2*n^2 - 12*n + 17)*a(n-3). - Vaclav Kotesovec, Jan 31 2014
a(n) ~ 4 * (n-2)!. - Vaclav Kotesovec, Jan 31 2014
EXAMPLE
The matrix corresponding to {4,3,1,2} disconnects its zeros since the 0 in the bottom left is not horizontally or vertically adjacent to another 0. In contrast, the matrix corresponding to {4,2,1,3} connects its zeros.
MATHEMATICA
Table[4*Sum[i!, {i, n - 2}] - 2*(n - 2)*Sum[i!, {i, 0, n - 4}] + 2*Sum[i!, {i, n - 3}] + 2, {n, 2, 25}] (* T. D. Noe, Nov 16 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Brian Hopkins, Nov 16 2012
STATUS
approved