A182866 Number of edges in the n^2 X n^2 Sudoku graph.

0, 56, 810, 4992, 20000, 61560, 158466, 358400, 734832, 1395000, 2488970, 4219776, 6854640, 10737272, 16301250, 24084480, 34744736, 49076280, 68027562, 92720000, 124467840, 164799096, 215477570, 278525952, 356250000, 451263800, 566516106, 705317760

Offset: 1

Author

Douglas Smith, Feb 01 2011

Keywords

• easy
• nonn

Examples

			For the standard Sudoku (n=3) there are 81 vertices. Each vertex is connected to 8 others within its own square, and 12 others in its row and column. Dividing by 2 gives 810 edges.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A000583 (number of vertices), A140676 (degree of each vertex).

Programs

Mathematica

Table[n^4/2 (-1-2n+3n^2),{n,30}] (* or *) LinearRecurrence[ {7,-21,35,-35,21,-7,1},{0,56,810,4992,20000,61560,158466},30] (* Harvey P. Dale, Oct 30 2011 *)

PARI

Vec(2*x^2*(28+209*x+249*x^2+53*x^3+x^4)/(1-x)^7+O(x^99)) \\ Charles R Greathouse IV, Jan 25 2012

Formula

a(n) = (1/2)*n^4*(-1 - 2*n + 3*n^2).

a(1)=0, a(2)=56, a(3)=810, a(4)=4992, a(5)=20000, a(6)=61560, a(7)=158466, a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Harvey P. Dale, Oct 30 2011

G.f.: 2*x^2*(28 + 209*x + 249*x^2 + 53*x^3 + x^4)/(1-x)^7. - Colin Barker, Jan 25 2012