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A182866
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Number of edges in the n^2 X n^2 Sudoku graph.
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2
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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
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OFFSET
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1,2
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LINKS
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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).
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FORMULA
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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
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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easy,nonn
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AUTHOR
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Douglas Smith, Feb 01 2011
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STATUS
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approved
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