OFFSET
0,5
COMMENTS
The 4 X 4 Sudoku graph is a septic graph on 16 vertices and 56 edges. a(n) gives the number of 4 X 4 Sudoku solutions, if each of up to n numbers is allowed only once in every row, column and block.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Timme, Marc; van Bussel, Frank; Fliegner, Denny; Stolzenberg, Sebastian (2009) "Counting complex disordered states by efficient pattern matching: chromatic polynomials and Potts partition functions", New J. Phys. 11 023001, doi: 10.1088/1367-2630/11/2/023001.
Eric Weisstein's World of Mathematics, Chromatic Polynomial
Wikipedia, Mathematics of Sudoku
Wikipedia, Sudoku
Wikipedia, Sudoku algorithms
Index entries for linear recurrences with constant coefficients, signature (17,-136,680, -2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380, -680,136,-17,1).
FORMULA
a(n) = n^16 -56*n^15 + ... (see Maple program).
G.f.: -96*x^4*(343316843*x^12 +4128584684*x^11 +20203233398*x^10 +50370257700*x^9 +68017469565*x^8 +50271571704*x^7 +20027437332*x^6 +4145554824*x^5 +419198325*x^4 +18781660*x^3 +320278*x^2 +1684*x +3)/ (x-1)^17. - Colin Barker, Aug 04 2012
EXAMPLE
For n=4 colors one of the 288 possible colorings is given by this Sudoku:
+---+---+
|1 2|3 4|
|4 3|2 1|
+---+---+
|3 1|4 2|
|2 4|1 3|
+---+---+ .
MAPLE
a:= n-> n^16 -56*n^15 +1492*n^14 -25072*n^13 +296918*n^12 -2621552*n^11 +17795572*n^10 -94352168*n^9 +392779169*n^8 -1279118840*n^7 +3217758336*n^6 -6107865464*n^5 +8413745644*n^4 -7877463064*n^3 +4436831332*n^2 -1117762248*n: seq(a(n), n=0..20);
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Alois P. Heinz, Apr 09 2009
STATUS
approved