A360875 Array read by antidiagonals: T(m,n) is the number of connected dominating sets in the rook graph K_m X K_n.
1, 3, 3, 7, 9, 7, 15, 39, 39, 15, 31, 177, 325, 177, 31, 63, 783, 2931, 2931, 783, 63, 127, 3369, 26077, 51465, 26077, 3369, 127, 255, 14199, 225459, 894675, 894675, 225459, 14199, 255, 511, 58977, 1901725, 15195897, 30331861, 15195897, 1901725, 58977, 511
Offset: 1
Examples
Array begins: ======================================================= m\n| 1 2 3 4 5 6 ... ---+--------------------------------------------------- 1 | 1 3 7 15 31 63 ... 2 | 3 9 39 177 783 3369 ... 3 | 7 39 325 2931 26077 225459 ... 4 | 15 177 2931 51465 894675 15195897 ... 5 | 31 783 26077 894675 30331861 1010163363 ... 6 | 63 3369 225459 15195897 1010163363 66273667449 ... ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 antidiagonals).
- Eric Weisstein's World of Mathematics, Connected Dominating Set
- Eric Weisstein's World of Mathematics, Rook Graph
Programs
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PARI
\\ S is A183109, T is A262307, U is this sequence. G(M,N=M)={S=matrix(M, N); T=matrix(M, N); U=matrix(M, N); for(m=1, M, for(n=1, N, S[m, n]=sum(j=0, m, (-1)^j*binomial(m, j)*(2^(m - j) - 1)^n); T[m, n]=S[m, n]-sum(i=1, m-1, sum(j=1, n-1, T[i, j]*S[m-i, n-j]*binomial(m-1, i-1)*binomial(n, j))); U[m, n]=sum(i=1, m, binomial(m, i)*T[i, n])+sum(j=1, n, binomial(n, j)*T[m, j])-T[m, n] )); U } { my(A=G(7)); for(n=1, #A~, print(A[n,])) }