A183680 T(n,k)=Number of (n+1)X(k+1) 0..7 arrays with every 2X2 subblock summing to 14

344, 2080, 2080, 13448, 10088, 13448, 90784, 54496, 54496, 90784, 631784, 316232, 252920, 316232, 631784, 4497760, 1931680, 1287136, 1287136, 1931680, 4497760, 32592008, 12267368, 7003928, 5836328, 7003928, 12267368, 32592008, 239551264

Offset

1,1

Comments

Table starts

.........344.......2080......13448.....90784....631784...4497760..32592008

........2080......10088......54496....316232...1931680..12267368..80331616

.......13448......54496.....252920...1287136...7003928..40112416.239241080

.......90784.....316232....1287136...5836328..28648864.149494472.819074656

......631784....1931680....7003928..28648864.128141624.614337760

.....4497760...12267368...40112416.149494472.614337760

....32592008...80331616..239241080.819074656

...239551264..539328392.1474919776

..1781373224.3696942880

.13376585440

Links

R. H. Hardin, Table of n, a(n) for n = 1..59

Formula

Empirical, for every row and column: a(n)=36*a(n-1)-546*a(n-2)+4536*a(n-3)-22449*a(n-4)+67284*a(n-5)-118124*a(n-6)+109584*a(n-7)-40320*a(n-8)

The coefficient of a(n-i) is -s(9,9-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
..7..0..7....3..6..4....5..3..3....6..3..2....7..0..5....1..5..0....2..5..2
..1..6..1....4..1..3....5..1..7....3..2..7....3..4..5....6..2..7....0..7..0
..5..2..5....5..4..6....7..1..5....4..5..0....6..1..4....6..0..5....3..4..3
..1..6..1....3..2..2....2..4..4....2..3..6....1..6..3....1..7..2....1..6..1

Crossrefs

Sequence in context: A236090 A237378 A237243 * A183674 A245994 A246630

Adjacent sequences: A183677 A183678 A183679 * A183681 A183682 A183683

Keyword

nonn,tabl

Author

R. H. Hardin Jan 06 2011

Status

approved