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A251373 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to 1 2 3 4 5 6 or 7.

%I A251373 #6 Jun 02 2025 10:24:01
%S A251373 79,695,695,6113,17969,6113,53769,464393,464393,53769,472943,12002283,
%T A251373 35257505,12002283,472943,4159927,310199103,2676962017,2676962017,
%U A251373 310199103,4159927,36590017,8017100977,203249994369,597108952883
%N A251373 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to 1 2 3 4 5 6 or 7.
%C A251373 Table starts
%C A251373 ......79........695...........6113.............53769...............472943
%C A251373 .....695......17969.........464393..........12002283............310199103
%C A251373 ....6113.....464393.......35257505........2676962017.........203249994369
%C A251373 ...53769...12002283.....2676962017......597108952883......133187012365193
%C A251373 ..472943..310199103...203249994369...133187012365193....87274898497023663
%C A251373 .4159927.8017100977.15431888950873.29707797738391051.57189617044768555919
%H A251373 R. H. Hardin, <a href="/A251373/b251373.txt">Table of n, a(n) for n = 1..312</a>
%F A251373 Empirical for column k:
%F A251373 k=1: a(n) = 8*a(n-1) +7*a(n-2)
%F A251373 k=2: a(n) = 24*a(n-1) +49*a(n-2) -34*a(n-3)
%F A251373 k=3: a(n) = 66*a(n-1) +746*a(n-2) +660*a(n-3) -6281*a(n-4) +3690*a(n-5)
%F A251373 k=4: [order 10]
%F A251373 k=5: [order 20]
%e A251373 Some solutions for n=2 k=4
%e A251373 ..0..0..0..0..1....0..0..0..0..1....0..0..0..0..0....0..0..0..0..2
%e A251373 ..2..2..1..0..0....2..2..0..2..2....2..0..2..1..0....0..2..1..1..2
%e A251373 ..1..2..2..2..0....1..1..2..1..2....2..1..2..2..1....1..1..2..1..2
%K A251373 nonn,tabl
%O A251373 1,1
%A A251373 _R. H. Hardin_, Dec 01 2014