A183662 T(n,k) = Number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock summing to 10.

146, 666, 666, 3254, 2442, 3254, 16626, 9990, 9990, 16626, 87686, 43986, 35162, 43986, 87686, 473586, 204246, 135966, 135966, 204246, 473586, 2605574, 987762, 563114, 469146, 563114, 987762, 2605574, 14548626, 4934070, 2458590, 1755246

Offset

1,1

Comments

Table starts

.......146.......666.......3254.....16626.....87686....473586...2605574

.......666......2442.......9990.....43986....204246....987762...4934070

......3254......9990......35162....135966....563114...2458590..11196842

.....16626.....43986.....135966....469146...1755246...6990906..29275086

.....87686....204246.....563114...1755246...5992826..21960366..85187834

....473586....987762....2458590...6990906..21960366..74549082.269462670

...2605574...4934070...11196842..29275086..85187834.269462670

..14548626..25308786...52793406.127755066.346364046

..82214726.132730326..256308074.577190766

.469200306.709335282.1275989790

Links

R. H. Hardin, Table of n, a(n) for n = 1..83

Formula

Empirical, for every row and column: a(n)=21*a(n-1)-175*a(n-2)+735*a(n-3)-1624*a(n-4)+1764*a(n-5)-720*a(n-6).

The coefficient of a(n-i) is -s(7,7-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 2 X 2 blocks summing to 2z, the coefficients are -s(z+2,z+2-i).

Example

Some solutions for 4 X 3
..3..3..2....2..4..3....4..1..5....2..1..4....4..3..2....2..3..2....3..1..3
..0..4..1....4..0..3....2..3..1....5..2..3....3..0..5....5..0..5....4..2..4
..5..1..4....4..2..5....4..1..5....3..0..5....3..4..1....1..4..1....3..1..3
..2..2..3....1..3..0....3..2..2....5..2..3....1..2..3....4..1..4....1..5..1

Crossrefs

Sequence in context: A211838 A158132 A043431 * A183654 A183653 A231243

Adjacent sequences: A183659 A183660 A183661 * A183663 A183664 A183665

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 06 2011

Status

approved