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Number of (n+2)X(4+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00001111
1

%I #4 Jul 23 2015 13:11:30

%S 436,700,2014,4633,5326,12858,32488,46993,89140,223963,379838,657619,

%T 1551102,2943373,5005180,10882474,22057020,38567570,77971796,

%U 162031604,295335654,570612861,1181007446,2235793266,4234428804,8612184438

%N Number of (n+2)X(4+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00001111

%C Column 4 of A260370

%H R. H. Hardin, <a href="/A260366/b260366.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-2) +8*a(n-3) +12*a(n-4) -13*a(n-5) -41*a(n-6) -74*a(n-7) -48*a(n-8) +117*a(n-9) +285*a(n-10) +320*a(n-11) +86*a(n-12) -554*a(n-13) -1101*a(n-14) -814*a(n-15) +181*a(n-16) +1674*a(n-17) +2737*a(n-18) +1245*a(n-19) -1501*a(n-20) -3641*a(n-21) -4387*a(n-22) -604*a(n-23) +3881*a(n-24) +4764*a(n-25) +4047*a(n-26) -556*a(n-27) -4431*a(n-28) -3433*a(n-29) -2418*a(n-30) +457*a(n-31) +2649*a(n-32) +1428*a(n-33) +977*a(n-34) -28*a(n-35) -834*a(n-36) -270*a(n-37) -233*a(n-38) -54*a(n-39) +136*a(n-40) +20*a(n-41) +21*a(n-42) +7*a(n-43) -8*a(n-44) for n>46

%e Some solutions for n=4

%e ..1..1..0..0..1..1....0..0..0..0..0..1....0..0..0..0..1..0....1..0..0..0..0..0

%e ..0..1..0..0..1..0....1..1..0..0..1..1....0..1..0..0..1..0....1..1..0..0..1..1

%e ..0..0..0..0..0..0....0..0..0..0..1..1....0..1..0..0..0..0....0..0..0..0..0..1

%e ..0..0..0..0..0..0....0..0..0..0..0..1....0..0..0..0..0..0....0..0..0..0..0..1

%e ..1..1..0..0..1..0....0..1..0..0..0..1....0..0..0..0..1..1....0..1..0..0..1..1

%e ..1..0..0..0..1..0....1..0..0..0..1..1....1..1..0..0..0..1....1..0..0..0..0..0

%Y Cf. A260370

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 23 2015