Displaying 1-10 of 15 results found.
Number of potential flows in n X n array with integer velocities in -14..14, i.e., number of n X n arrays with adjacent elements differing by no more than 14, counting arrays differing by a constant only once.
+10
18
1, 16269, 105227044417, 278175212679968120043
Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the staggered hexagonal square grid graph SH_(k,k).
+10
14
1, 0, 2, 0, 0, 3, 0, 0, 6, 4, 0, 0, 6, 48, 5, 0, 0, 6, 1056, 180, 6, 0, 0, 6, 45696, 32940, 480, 7, 0, 0, 6, 4038432, 30847500, 393600, 1050, 8, 0, 0, 6, 743601024, 148046704020, 3312560640, 2735250, 2016, 9
COMMENTS
The staggered hexagonal square grid graph SH_(n,n) has n^2 = A000290(n) vertices and (n-1)*(3*n-1) = A045944(n-1) edges; see A212194 for example. The chromatic polynomial of SH_(n,n) has n^2+1 = A002522(n) coefficients. A differs from A212163 first at (n,k) = (4,5): A(4,5) = 4038432, A212163(4,5) = 4034304.
EXAMPLE
Square array A(n,k) begins:
1, 0, 0, 0, 0, ...
2, 0, 0, 0, 0, ...
3, 6, 6, 6, 6, ...
4, 48, 1056, 45696, 4038432, ...
5, 180, 32940, 30847500, 148046704020, ...
6, 480, 393600, 3312560640, 286170443437440, ...
7, 1050, 2735250, 123791435250, 97337320223288250, ...
CROSSREFS
Rows n=1-10, 16-18 give: A000007, A000038, A040006, 4* A068283, 5* A068284, 6* A068285, 7* A068286, 8* A068287, 9* A068288, 10* A068289, 16* A068290, 17* A068291, 18* A068292.
Number of potential flows in n X n array with integer velocities in -1..1, i.e., number of n X n arrays with adjacent elements differing by no more than 1, counting arrays differing by a constant only once.
+10
5
1, 19, 1665, 690437, 1366395515, 12961320464027, 590771311004409091, 129585582154154757804255, 136932044780329080616264070553, 697547669137459516115242710064880165
Number of potential flows in n X n array with integer velocities in -5..5, i.e., number of n X n arrays with adjacent elements differing by no more than 5, counting arrays differing by a constant only once.
+10
1
1, 891, 45642289, 138190481342321, 24953087551680958151267
Number of potential flows in n X n array with integer velocities in -2..2, i.e., number of n X n arrays with adjacent elements differing by no more than 2, counting arrays differing by a constant only once.
+10
0
1, 85, 87825, 1133641543, 184422574177355, 379827509377146575439, 9928923943603018785634645661
Number of potential flows in n X n array with integer velocities in -3..3, i.e., number of n X n arrays with adjacent elements differing by no more than 3, counting arrays differing by a constant only once.
+10
0
1, 231, 1253329, 164185416899, 523957519578572209, 40918963843906494595507077
Number of potential flows in n X n array with integer velocities in -4..4, i.e., number of n X n arrays with adjacent elements differing by no more than 4, counting arrays differing by a constant only once.
+10
0
1, 489, 9230193, 6913624013061, 207345516734034667209
Number of potential flows in n X n array with integer velocities in -6..6, i.e., number of n X n arrays with adjacent elements differing by no more than 6, counting arrays differing by a constant only once.
+10
0
1, 1469, 172989921, 1678843050246451, 1354915464537160758459123
Number of potential flows in n X n array with integer velocities in -7..7, i.e., number of n X n arrays with adjacent elements differing by no more than 7, counting arrays differing by a constant only once.
+10
0
1, 2255, 542131425, 14285299502131463
Number of potential flows in n X n array with integer velocities in -8..8, i.e., number of n X n arrays with adjacent elements differing by no more than 8, counting arrays differing by a constant only once.
+10
0
1, 3281, 1473095713, 93044501704039945
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