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%I #6 Sep 04 2022 08:28:31
%S 8,64,512,3772,32768,262144,2097152,16777216,134140928,1073741824,
%T 8589934592,68719476736,549755813888,4398033385216,35184372088832,
%U 281474976710656,2251799813685248,18014398509481984,144115185909972992
%N Sum of neighbor maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal, diagonal and antidiagonal neighbors in a random 0..2 n X 3 array.
%C Column 3 of A221666.
%H R. H. Hardin, <a href="/A221664/b221664.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) +360*a(n-5) -2880*a(n-6) -47232*a(n-10) +377856*a(n-11) +2872320*a(n-15) -22978560*a(n-16) -92491776*a(n-20) +739934208*a(n-21) +1689550848*a(n-25) -13516406784*a(n-26) -18150850560*a(n-30) +145206804480*a(n-31) +113850187776*a(n-35) -910801502208*a(n-36) -386547056640*a(n-40) +3092376453120*a(n-41) +549755813888*a(n-45) -4398046511104*a(n-46).
%e Some solutions for n=3
%e ..1..1..1....1..0..0....0..0..1....0..1..1....0..0..1....1..0..0....1..1..0
%e ..0..1..0....0..0..0....0..0..0....0..1..0....0..0..1....1..1..1....1..1..0
%e ..0..0..1....1..1..1....0..1..1....1..0..1....1..0..1....1..1..1....0..0..0
%Y Cf. A221666.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 21 2013
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