|
Search: id:A159299
|
|
|
| A159299 |
|
Number of n-colorings of the 4 X 4 Sudoku graph. |
|
+0
1
|
|
| 0, 0, 0, 0, 288, 166560, 33539040, 2350746720, 75756999360, 1388552614848, 16744788486720, 146769785743680, 1002373493948640, 5606534724167520, 26640793339768608, 110556058012152480, 409297168707073920
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
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
|
Wikipedia "Mathematics of Sudoku"
Weisstein, Eric W. "Chromatic Polynomial".
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.
|
|
FORMULA
|
a(n) = n^16 -56*n^15 + ... (see Maple program).
|
|
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
|
Sequence in context: A163007 A069329 A037946 this_sequence A047805 A008695 A107739
Adjacent sequences: A159296 A159297 A159298 this_sequence A159300 A159301 A159302
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Alois P. Heinz (heinz(AT)hs-heilbronn.de), Apr 09 2009
|
|
|
Search completed in 0.002 seconds
|
