0,5

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals)

Eric Weisstein's World of Mathematics, Irredundant Set.

Eric Weisstein's World of Mathematics, Rook Complement Graph.

T(n,m) = n*(2^m-1) + m*(2^n-1) - n*m + binomial(n,2)*binomial(m,2) + 6*binomial(n,3)*binomial(m,3) + 6*binomial(n,2)*binomial(m,3) + 6*binomial(n,3)*binomial(m,2) + 6*binomial(n,4)*binomial(m,2) + 6*binomial(n,2)*binomial(m,4) + 1 for n >= 4, m >= 4.

Array begins:

===============================================

n\m | 0 1 2 3 4 5 6 7 ...

----+------------------------------------------

0 | 1 1 1 1 1 1 1 1 ...

1 | 1 2 4 8 16 32 64 128 ...

2 | 1 4 9 24 77 178 373 724 ...

3 | 1 8 24 94 284 624 1234 2258 ...

4 | 1 16 77 284 777 1620 3049 5332 ...

5 | 1 32 178 624 1620 3286 6022 10268 ...

6 | 1 64 373 1234 3049 6022 10771 17962 ...

7 | 1 128 724 2258 5332 10268 17962 29366 ...

...

(PARI) T(n, m) = {n*(2^m-1) + m*(2^n-1) - n*m + if(n>2&&m>2, 6, if(n+m>4, 2))*binomial(n, 2)*binomial(m, 2) + 6*binomial(n, 3)*binomial(m, 3) + if(m>3, 6*binomial(n, 2)*binomial(m, 3)) + if(n>3, 6*binomial(n, 3)*binomial(m, 2)) + 6*binomial(n, 4)*binomial(m, 2) + 6*binomial(n, 2)*binomial(m, 4) + 1}

Main diagonal is A291622.

Columns 0..2 are A000012, A000079, A290710.

Cf. A384123.

Sequence in context: A126770 A202979 A384120 * A306326 A156006 A137854

Adjacent sequences: A384121 A384122 A384123 * A384125 A384126 A384127

nonn,tabl

Andrew Howroyd, May 22 2025

approved