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A217447 Number of n x n permutation matrices that disconnect their zeros. 0
2, 6, 12, 32, 120, 580, 3392, 23244, 182776, 1622468, 16045200, 174894172, 2082824744, 26902998516, 374570250688, 5591767768460, 89095070783832, 1509041577895204, 27073887615758576, 512898265609845948, 10230945527263709320, 214337863242231108692 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..23.

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

Terms from A007489 in formula.

Sequence in context: A304961 A032178 A102881 * A057579 A096610 A164099

Adjacent sequences:  A217444 A217445 A217446 * A217448 A217449 A217450

KEYWORD

easy,nonn

AUTHOR

Brian Hopkins, Nov 16 2012

STATUS

approved

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Last modified May 25 03:50 EDT 2019. Contains 323539 sequences. (Running on oeis4.)