A183672 T(n,k) = number of (n+1) X (k+1) 0..6 arrays with every 2 X 2 subblock summing to 12.

231, 1225, 1225, 6951, 5215, 6951, 41209, 24745, 24745, 41209, 251991, 126223, 100935, 126223, 251991, 1577065, 678265, 451801, 451801, 678265, 1577065, 10049991, 3791935, 2163831, 1803007, 2163831, 3791935, 10049991, 64979929

Offset

1,1

Comments

Table starts

........231......1225......6951.....41209....251991...1577065..10049991

.......1225......5215.....24745....126223....678265...3791935..21874825

.......6951.....24745....100935....451801...2163831..10914505..57370215

......41209....126223....451801...1803007...7794409..35840623.173139001

.....251991....678265...2163831...7794409..30722151.129866905.580718871

....1577065...3791935..10914505..35840623.129866905

...10049991..21874825..57370215.173139001

...64979929.129463663.311907001

..425156151.782782105

.2809324105

Links

R. H. Hardin, Table of n, a(n) for n = 1..60

Formula

Empirical, for every row and column: a(n) = 28*a(n-1)-322*a(n-2)+1960*a(n-3)-6769*a(n-4)+13132*a(n-5)-13068*a(n-6)+5040*a(n-7).

The coefficient of a(n-i) is -s(8,8-i), s() being the Stirling number of the first kind, via D. S. McNeil and M. F. Hasler in the Sequence Fans Mailing List.

For a 0..z array with 2X2 blocks summing to 2z, the coefficients are -s(z+2,z+2-i).

Example

Some solutions for 4X3
..4..1..5....5..2..5....2..2..1....6..2..4....3..1..5....5..1..5....0..6..1
..6..1..5....2..3..2....3..5..4....2..2..4....3..5..1....6..0..6....3..3..2
..3..2..4....4..3..4....4..0..3....4..4..2....4..0..6....3..3..3....0..6..1
..5..2..4....1..4..1....2..6..3....3..1..5....6..2..4....1..5..1....3..3..2

Crossrefs

Cf. A183663, A183664, A183665, A183666, A183667, A183668, A183669, A183670, A183671.

Sequence in context: A258167 A287472 A350368 * A183664 A260302 A211717

Adjacent sequences: A183669 A183670 A183671 * A183673 A183674 A183675

Keyword

nonn,tabl,changed

Author

R. H. Hardin, Jan 06 2011

Status

approved