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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

%I #7 Mar 31 2012 12:35:53

%S 344,2080,2080,13448,10088,13448,90784,54496,54496,90784,631784,

%T 316232,252920,316232,631784,4497760,1931680,1287136,1287136,1931680,

%U 4497760,32592008,12267368,7003928,5836328,7003928,12267368,32592008,239551264

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

%C Table starts

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

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

%C .......13448......54496.....252920...1287136...7003928..40112416.239241080

%C .......90784.....316232....1287136...5836328..28648864.149494472.819074656

%C ......631784....1931680....7003928..28648864.128141624.614337760

%C .....4497760...12267368...40112416.149494472.614337760

%C ....32592008...80331616..239241080.819074656

%C ...239551264..539328392.1474919776

%C ..1781373224.3696942880

%C .13376585440

%H R. H. Hardin, <a href="/A183680/b183680.txt">Table of n, a(n) for n = 1..59</a>

%F 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)

%F 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.

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

%e Some solutions for 4X3

%e ..7..0..7....3..6..4....5..3..3....6..3..2....7..0..5....1..5..0....2..5..2

%e ..1..6..1....4..1..3....5..1..7....3..2..7....3..4..5....6..2..7....0..7..0

%e ..5..2..5....5..4..6....7..1..5....4..5..0....6..1..4....6..0..5....3..4..3

%e ..1..6..1....3..2..2....2..4..4....2..3..6....1..6..3....1..7..2....1..6..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 06 2011

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)