%I #22 Jun 13 2015 00:53:41
%S 0,56,810,4992,20000,61560,158466,358400,734832,1395000,2488970,
%T 4219776,6854640,10737272,16301250,24084480,34744736,49076280,
%U 68027562,92720000,124467840,164799096,215477570,278525952,356250000,451263800,566516106,705317760
%N Number of edges in the n^2 X n^2 Sudoku graph.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = (1/2)*n^4*(-1 - 2*n + 3*n^2).
%F 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
%F G.f.: 2*x^2*(28 + 209*x + 249*x^2 + 53*x^3 + x^4)/(1-x)^7. - _Colin Barker_, Jan 25 2012
%e 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.
%t 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 *)
%o (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
%Y Cf. A000583 (number of vertices), A140676 (degree of each vertex).
%K easy,nonn
%O 1,2
%A _Douglas Smith_, Feb 01 2011