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A220801 Sum of neighbor maps: number of nX2 binary arrays indicating the locations of corresponding elements equal to the sum mod 4 of their horizontal and vertical neighbors in a random 0..3 nX2 array.

%I A220801 #7 Jul 23 2025 01:29:42
%S A220801 2,16,48,256,928,4096,15820,65536,259584,1048576,4182016,16777216,
%T A220801 67051520,268435456,1073476576,4294967296,17178689536,68719476736,
%U A220801 274872664064,1099511627776,4398023442432,17592186044416,70368643424320
%N A220801 Sum of neighbor maps: number of nX2 binary arrays indicating the locations of corresponding elements equal to the sum mod 4 of their horizontal and vertical neighbors in a random 0..3 nX2 array.
%C A220801 Column 2 of A220805
%H A220801 R. H. Hardin, <a href="/A220801/b220801.txt">Table of n, a(n) for n = 1..210</a>
%F A220801 Empirical: a(n) = 4*a(n-1) +8*a(n-2) -32*a(n-3) -16*a(n-4) +64*a(n-5) +44*a(n-8) -176*a(n-9) -352*a(n-10) +1408*a(n-11) +704*a(n-12) -2816*a(n-13) -688*a(n-16) +2752*a(n-17) +5504*a(n-18) -22016*a(n-19) -11008*a(n-20) +44032*a(n-21) +4672*a(n-24) -18688*a(n-25) -37376*a(n-26) +149504*a(n-27) +74752*a(n-28) -299008*a(n-29) -14336*a(n-32) +57344*a(n-33) +114688*a(n-34) -458752*a(n-35) -229376*a(n-36) +917504*a(n-37) +16384*a(n-40) -65536*a(n-41) -131072*a(n-42) +524288*a(n-43) +262144*a(n-44) -1048576*a(n-45)
%e A220801 Some solutions for n=3
%e A220801 ..0..0....0..0....0..0....0..0....1..0....0..0....0..1....0..1....0..1....1..1
%e A220801 ..0..1....1..1....0..1....0..0....1..0....1..1....0..1....1..0....1..1....0..0
%e A220801 ..0..1....0..0....1..0....1..0....1..0....1..0....1..0....0..1....0..1....1..1
%K A220801 nonn
%O A220801 1,1
%A A220801 _R. H. Hardin_ Dec 21 2012