A183642 - OEIS

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

%S 44,136,136,452,340,452,1576,952,952,1576,5684,2884,2300,2884,5684,

%T 21016,9256,6136,6136,9256,21016,79172,31060,17612,14644,17612,31060,

%U 79172,302536,107992,53512,38056,38056,53512,107992,302536,1168724,386404

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock summing to 6

%C Table starts

%C ......44.....136.....452....1576.....5684....21016....79172...302536..1168724

%C .....136.....340.....952....2884.....9256....31060...107992...386404..1415176

%C .....452.....952....2300....6136....17612....53512...170300...563416..1926572

%C ....1576....2884....6136...14644....38056...105604...309016...945364..3004936

%C ....5684....9256...17612...38056....90524...231736...629132..1793416..5328764

%C ...21016...31060...53512..105604...231736...551380..1398952..3743524.10479256

%C ...79172..107992..170300..309016...629132..1398952..3333500..8411896.22294892

%C ..302536..386404..563416..945364..1793416..3743524..8411896.20077684.50494696

%C .1168724.1415176.1926572.3004936..5328764.10479256.22294892.50494696

%C .4552696.5281780.6776872.9877924.16413016.30483700.61632712

%H R. H. Hardin, <a href="/A183642/b183642.txt">Table of n, a(n) for n = 1..143</a>

%F Empirical, for every row and column: a(n)=10*a(n-1)-35*a(n-2)+50*a(n-3)-24*a(n-4)

%F The coefficient of a(n-i) is -s(5,5-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 ..2..2..1....1..1..2....1..1..0....2..1..1....1..3..2....3..1..2....2..1..3

%e ..2..0..3....2..2..1....1..3..2....2..1..3....1..1..0....0..2..1....3..0..2

%e ..1..3..0....2..0..3....1..1..0....3..0..2....1..3..2....1..3..0....2..1..3

%e ..1..1..2....3..1..2....1..3..2....1..2..2....1..1..0....2..0..3....1..2..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 06 2011