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

1,2

Links

Table of n, a(n) for n=1..28.

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

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A227059 A285155 A278197 * A008389 A338002 A351410

Adjacent sequences: A182863 A182864 A182865 * A182867 A182868 A182869

Keyword

easy,nonn

Author

Douglas Smith, Feb 01 2011

Status

approved