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A204076 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.

%I A204076 #7 Jul 22 2025 17:45:35
%S A204076 8,38,38,188,329,188,938,2882,2882,938,4688,25277,45056,25277,4688,
%T A204076 23438,221726,706454,706454,221726,23438,117188,1944977,11081828,
%U A204076 19934369,11081828,1944977,117188,585938,17061338,173848010,563880962,563880962
%N A204076 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.
%C A204076 Table starts
%C A204076 ......8........38.........188............938.............4688
%C A204076 .....38.......329........2882..........25277...........221726
%C A204076 ....188......2882.......45056.........706454.........11081828
%C A204076 ....938.....25277......706454.......19934369........563880962
%C A204076 ...4688....221726....11081828......563880962......28864215128
%C A204076 ..23438...1944977...173848010....15960507749....1480470688070
%C A204076 .117188..17061338..2727300008...451830740558...75985220860460
%C A204076 .585938.149662085.42785526110.12791537916233.3900809853901802
%H A204076 R. H. Hardin, <a href="/A204076/b204076.txt">Table of n, a(n) for n = 1..220</a>
%F A204076 Empirical for column k:
%F A204076 k=1: a(n) = (3*5^n+1)/2
%F A204076 k=2: a(n) = 10*a(n-1) -11*a(n-2) +2*a(n-3)
%F A204076 k=3: a(n) = 20*a(n-1) -73*a(n-2) +86*a(n-3) -32*a(n-4)
%F A204076 k=4: a(n) = 32*a(n-1) -55*a(n-2) -1588*a(n-3) +5428*a(n-4) -2664*a(n-5) -3936*a(n-6) +3040*a(n-7) -256*a(n-8)
%F A204076 k=5: (order 13 recurrence)
%F A204076 k=6: (order 29 recurrence)
%F A204076 k=7: (order 55 recurrence)
%e A204076 Some solutions for n=4 k=3
%e A204076 ..0..0..0..0....0..0..0..0....0..0..1..2....0..0..0..1....0..0..1..2
%e A204076 ..0..0..0..0....1..0..0..0....2..0..0..1....2..0..1..0....2..0..0..1
%e A204076 ..1..0..0..2....2..1..0..0....1..2..0..0....0..2..0..1....0..1..0..0
%e A204076 ..2..1..0..0....2..2..1..0....2..2..2..0....2..0..0..0....0..0..0..0
%e A204076 ..1..2..1..0....2..0..2..1....0..2..2..2....2..2..0..1....2..0..0..0
%Y A204076 Column 1 is A199213
%K A204076 nonn,tabl
%O A204076 1,1
%A A204076 _R. H. Hardin_ Jan 10 2012