A222340 T(n,k) = number of n X k 0..6 arrays with no entry increasing mod 7 by 6 rightwards or downwards, starting with upper left zero.
1, 6, 6, 36, 186, 36, 216, 5766, 5766, 216, 1296, 178746, 923526, 178746, 1296, 7776, 5541126, 147918906, 147918906, 5541126, 7776, 46656, 171774906, 23691810366, 122408393436, 23691810366, 171774906, 46656, 279936, 5325022086
Offset: 1
Examples
Table starts .......1.............6...................36........................216 .......6...........186.................5766.....................178746 ......36..........5766...............923526..................147918906 .....216........178746............147918906...............122408393436 ....1296.......5541126..........23691810366............101297497221786 ....7776.....171774906........3794659477146..........83827445649884946 ...46656....5325022086......607781352505806.......69370328359709445996 ..279936..165075684666....97346856728146986....57406526220963704077986 .1679616.5117346224646.15591808593304758846.47506035082750189614687546 ... Some solutions for n=3, k=4: ..0..0..2..0....0..2..2..0....0..0..0..0....0..2..0..0....0..2..0..0 ..0..5..3..0....0..2..5..0....0..1..5..0....0..5..0..0....0..0..5..0 ..3..1..4..5....4..4..2..3....3..6..1..4....2..2..2..2....4..1..3..4
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..325 (terms 1..84 from R. H. Hardin)
Crossrefs
Formula
T(n, k) = 6 * (120*A198723(n,k) - 60*A198906(n,k) - 40*A198715(n,k) - 15*A207997(n,k) - 4) for n*k > 1. - Andrew Howroyd, Jun 27 2017
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