OFFSET
1,10
COMMENTS
The recurrence for the second row comes from Doron Zeilberger's MENAGE program, available via the arXiv reference.
LINKS
D. Zeilberger, Automatic Enumeration of Generalized Menage Numbers, arXiv preprint arXiv:1401.1089 [math.CO], 2014.
FORMULA
T(n,n) = A000166(n) for n >= 1.
T(1,k) = A000179(k).
T(k-1,k) = A000179(k) for k >= 2.
T(n,k) = T(n+k, k).
T(2,k) = k*T(2,k-1) + 3*T(2,k-2) + (-2*k+6)*T(2,k-3) - 3*T(2,k-4) + (k-6)*T(2,k-5) + T(2,k-6) for k > 8.
T(n,k) = A277256(gcd(n,k),k/gcd(n,k)). - Pontus von Brömssen, May 31 2022
EXAMPLE
Table begins:
n\k | 1 2 3 4 5 6 7 8
----+--------------------------
1 | 0 0 1 2 13 80 579 4738
2 | 0 1 1 4 13 82 579 4740
3 | 0 0 2 2 13 80 579 4738
4 | 0 1 1 9 13 82 579 4752
5 | 0 0 1 2 44 80 579 4738
6 | 0 1 2 4 13 265 579 4740
7 | 0 0 1 2 13 80 1854 4738
8 | 0 1 1 9 13 82 579 14833
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Kagey, Feb 11 2021
STATUS
approved