A384120 Array read by antidiagonals: T(n,m) is the number of cliques in the n X m rook graph K_n X K_m.
1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 9, 8, 1, 1, 16, 18, 18, 16, 1, 1, 32, 35, 34, 35, 32, 1, 1, 64, 68, 62, 62, 68, 64, 1, 1, 128, 133, 114, 105, 114, 133, 128, 1, 1, 256, 262, 214, 180, 180, 214, 262, 256, 1, 1, 512, 519, 410, 319, 286, 319, 410, 519, 512, 1
Offset: 0
Examples
Array begins: ================================================= n\m | 0 1 2 3 4 5 6 7 8 ... ----+------------------------------------------- 0 | 1 1 1 1 1 1 1 1 1 ... 1 | 1 2 4 8 16 32 64 128 256 ... 2 | 1 4 9 18 35 68 133 262 519 ... 3 | 1 8 18 34 62 114 214 410 798 ... 4 | 1 16 35 62 105 180 319 586 1109 ... 5 | 1 32 68 114 180 286 472 818 1484 ... 6 | 1 64 133 214 319 472 721 1162 1987 ... 7 | 1 128 262 410 586 818 1162 1730 2746 ... 8 | 1 256 519 798 1109 1484 1987 2746 4017 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals)
- Eric Weisstein's World of Mathematics, Clique.
- Eric Weisstein's World of Mathematics, Rook Graph.
Crossrefs
Programs
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PARI
T(n,m) = 1 + n*(2^m - 1) + m*(2^n - 1) - n*m
Formula
T(n,m) = 1 + n*(2^m - 1) + m*(2^n - 1) - n*m.
T(n,m) = T(m,n).
Comments