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A183680 T(n,k)=Number of (n+1)X(k+1) 0..7 arrays with every 2X2 subblock summing to 14 8
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified November 27 15:29 EST 2014. Contains 250224 sequences.