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A183672 T(n,k)=Number of (n+1)X(k+1) 0..6 arrays with every 2X2 subblock summing to 12 10

%I

%S 231,1225,1225,6951,5215,6951,41209,24745,24745,41209,251991,126223,

%T 100935,126223,251991,1577065,678265,451801,451801,678265,1577065,

%U 10049991,3791935,2163831,1803007,2163831,3791935,10049991,64979929

%N T(n,k)=Number of (n+1)X(k+1) 0..6 arrays with every 2X2 subblock summing to 12

%C Table starts

%C ........231......1225......6951.....41209....251991...1577065..10049991

%C .......1225......5215.....24745....126223....678265...3791935..21874825

%C .......6951.....24745....100935....451801...2163831..10914505..57370215

%C ......41209....126223....451801...1803007...7794409..35840623.173139001

%C .....251991....678265...2163831...7794409..30722151.129866905.580718871

%C ....1577065...3791935..10914505..35840623.129866905

%C ...10049991..21874825..57370215.173139001

%C ...64979929.129463663.311907001

%C ..425156151.782782105

%C .2809324105

%H R. H. Hardin, <a href="/A183672/b183672.txt">Table of n, a(n) for n = 1..60</a>

%F Empirical, for every row and column: a(n)=28*a(n-1)-322*a(n-2)+1960*a(n-3)-6769*a(n-4)+13132*a(n-5)-13068*a(n-6)+5040*a(n-7)

%F The coefficient of a(n-i) is -s(8,8-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 ..4..1..5....5..2..5....2..2..1....6..2..4....3..1..5....5..1..5....0..6..1

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Jan 06 2011

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Last modified August 14 18:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)