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A259427 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 0001 0011 or 0111.

%I A259427 #6 Jun 02 2025 11:51:34
%S A259427 13,43,43,142,243,142,469,1366,1366,469,1549,7695,12953,7695,1549,
%T A259427 5116,43347,123306,123306,43347,5116,16897,244228,1172659,1990133,
%U A259427 1172659,244228,16897,55807,1376077,11155819,32060569,32060569,11155819,1376077
%N A259427 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 0001 0011 or 0111.
%C A259427 Table starts
%C A259427 .....13.......43........142...........469............1549...............5116
%C A259427 .....43......243.......1366..........7695...........43347.............244228
%C A259427 ....142.....1366......12953........123306.........1172659...........11155819
%C A259427 ....469.....7695.....123306.......1990133........32060569..........516880938
%C A259427 ...1549....43347....1172659......32060569.......873754597........23840819225
%C A259427 ...5116...244228...11155819.....516880938.....23840819225......1101527291223
%C A259427 ..16897..1376077..106118138....8331704179....650266054724.....50866278137234
%C A259427 ..55807..7753553.1009466878..134312969201..17738788220867...2349427850331898
%C A259427 .184318.43687910.9602626846.2165188798924.483879193637566.108508759637883502
%H A259427 R. H. Hardin, <a href="/A259427/b259427.txt">Table of n, a(n) for n = 1..391</a>
%F A259427 Empirical for column k:
%F A259427 k=1: a(n) = 3*a(n-1) +a(n-2)
%F A259427 k=2: a(n) = 6*a(n-1) +2*a(n-2) -22*a(n-3) -6*a(n-4) +6*a(n-5) +a(n-6)
%F A259427 k=3: [order 8]
%F A259427 k=4: [order 20]
%F A259427 k=5: [order 32]
%F A259427 k=6: [order 62]
%e A259427 Some solutions for n=3 k=4
%e A259427 ..0..0..1..1..0....0..0..0..1..0....1..0..0..1..1....1..1..0..1..1
%e A259427 ..0..0..1..0..0....0..1..0..0..0....0..0..1..1..0....0..0..0..0..0
%e A259427 ..0..0..0..0..1....0..1..1..0..1....0..0..0..0..0....0..0..0..0..1
%e A259427 ..1..0..0..0..0....1..1..0..0..0....1..1..0..0..0....0..1..0..1..1
%Y A259427 Column 1 is A003688(n+2)
%K A259427 nonn,tabl
%O A259427 1,1
%A A259427 _R. H. Hardin_, Jun 26 2015