A303147
Number of total dominating sets in the n X n white bishop graph.
Original entry on oeis.org
1, 9, 143, 2699, 199095, 14042731, 3855890801, 1030417772377, 1084629728348393, 1128432868605656409, 4666227312488067563575, 19214059289771315688645819, 315759892137678954308707379391, 5181941387199963072391681357467099, 339917045534987610111076281503519527705
Offset: 2
A304564
Number of minimum total dominating sets in the n-triangular honeycomb bishop graph.
Original entry on oeis.org
0, 2, 2, 6, 75, 21, 208, 3950, 540, 11220, 314880, 25740, 917280, 36029700, 1965600, 107100000, 5627890800, 219769200, 16995484800, 1153034190000, 33844456800, 3525796058400, 300234909744000, 6868433880000, 927359072640000, 96883959332160000, 1776393899280000, 301733192320560000
Offset: 1
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T(n, k)=binomial(2*n-k, k)*binomial(n+k, n-k)*(2*(n-k))!*(2*k)!/(2^n)
b1(n) = sum(k=0, n, T(n,k))
b2(n) = sum(k=0, n, T(n,k)*(2*binomial(n+k+3,3)*(2*n-k+1) + 4*binomial(n+k+2,2)*binomial(2*n-k+2,2)))
b3(n) = sum(k=0, n, T(n,k)*(n+k)*(n+k+1)*(7*n-2*k+5)/3)
b4(n) = sum(k=0, n, T(n,k)*(2*binomial(n+k+4,4)*(2*n-k+1) + 24*binomial(n+k+2,2)*binomial(2*n-k+3,3)))
b5(n) = sum(k=0, n, T(n,k)*(40*binomial(n+k+6,6)*binomial(2*n-k+2,2) + 240*binomial(n+k+5,5)*binomial(2*n-k+3,3) + 304*binomial(n+k+4,4)*binomial(2*n-k+4,4)))
a(n) = my(t=n\3); if(n%3==0, b1(t), if(n%3==1, b2(t-1), b1(t+1) + b3(t) + b4(t-1) + b5(t-2))) \\ Andrew Howroyd, Apr 09 2025
A303145
Number of total dominating sets in the n X n black bishop graph.
Original entry on oeis.org
0, 1, 16, 143, 5468, 199095, 28216660, 3855890801, 2063573357664, 1084629728348393, 2257651988909632680, 4666227312488067563575, 38431519470524295069404276, 315759892137678954308707379391, 10364113216536074591340863505339180, 339917045534987610111076281503519527705
Offset: 1
A304558
Number of minimal total dominating sets in the n-triangular honeycomb bishop graph.
Original entry on oeis.org
0, 2, 4, 36, 203, 1854, 18188, 214646, 2909712
Offset: 1
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