A182406 Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the square grid graph G_(k,k).

1, 0, 2, 0, 2, 3, 0, 2, 18, 4, 0, 2, 246, 84, 5, 0, 2, 7812, 9612, 260, 6, 0, 2, 580986, 6000732, 142820, 630, 7, 0, 2, 101596896, 20442892764, 828850160, 1166910, 1302, 8, 0, 2, 41869995708, 380053267505964, 50820390410180, 38128724910, 6464682, 2408, 9

Offset: 1

Author

Alois P. Heinz, Apr 27 2012

Keywords

• nonn
• tabl

Comments

The square grid graph G_(n,n) has n^2 = A000290(n) vertices and 2*n*(n-1) = A046092(n-1) edges. The chromatic polynomial of G_(n,n) has n^2+1 = A002522(n) coefficients.

Examples

			Square array A(n,k) begins:
  1,   0,       0,           0,                 0, ...
  2,   2,       2,           2,                 2, ...
  3,  18,     246,        7812,            580986, ...
  4,  84,    9612,     6000732,       20442892764, ...
  5, 260,  142820,   828850160,    50820390410180, ...
  6, 630, 1166910, 38128724910, 21977869327169310, ...
		

Links

• Eric Weisstein's World of Mathematics, Grid Graph
• Wikipedia, Chromatic Polynomial

Crossrefs

Columns k=1-7 give: A000027, A091940, A068239*2, A068240*2, A068241*2, A068242*2, A068243*2.

Rows n=1-20 give: A000007, A007395, A068253*3, A068254*4, A068255*5, A068256*6, A068257*7, A068258*8, A068259*9, A068260*10, A068261*11, A068262*12, A068263*13, A068264*14, A068265*15, A068266*16, A068267*17, A068268*18, A068269*19, A068270*20.

Cf. A182368.