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A197053 Number of nX7 0..4 arrays with each element equal to the number its horizontal and vertical zero neighbors.

%I A197053 #8 Jul 22 2025 12:52:04
%S A197053 7,26,156,692,3580,17742,88056,439338,2192602,10912392,54394628,
%T A197053 271160024,1351103246,6733077562,33557756016,167232569172,
%U A197053 833404135538,4153405692526,20698773896328,103153449929238,514074952403758
%N A197053 Number of nX7 0..4 arrays with each element equal to the number its horizontal and vertical zero neighbors.
%C A197053 Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 0's, every 3 is next to 3 0's, every 4 is next to 4 0's
%C A197053 Column 7 of A197054
%H A197053 R. H. Hardin, <a href="/A197053/b197053.txt">Table of n, a(n) for n = 1..200</a>
%F A197053 Empirical: a(n) = 2*a(n-1) +9*a(n-2) +37*a(n-3) -187*a(n-5) -77*a(n-6) +248*a(n-7) +240*a(n-8) -1400*a(n-9) +564*a(n-10) +1220*a(n-11) +1358*a(n-12) -5000*a(n-13) +3019*a(n-14) +1209*a(n-15) +4104*a(n-16) -6840*a(n-17) +3995*a(n-18) +4214*a(n-19) -1497*a(n-20) -1140*a(n-21) -945*a(n-22) +1251*a(n-23) -2502*a(n-24) -60*a(n-25) -49*a(n-26) -272*a(n-27) +281*a(n-28) -376*a(n-29) -109*a(n-30) +103*a(n-31) +9*a(n-32) -27*a(n-33) -3*a(n-34) +6*a(n-35)
%e A197053 Some solutions for n=4
%e A197053 ..0..2..1..0..1..2..0....0..1..1..1..0..3..0....0..2..0..3..0..3..0
%e A197053 ..3..0..2..1..2..0..3....1..2..0..1..3..0..2....1..1..2..0..4..0..3
%e A197053 ..0..4..0..3..0..4..0....2..0..3..1..0..2..1....2..0..2..2..0..4..0
%e A197053 ..2..0..3..0..3..0..2....0..3..0..1..1..1..0....0..3..0..1..2..0..2
%K A197053 nonn
%O A197053 1,1
%A A197053 _R. H. Hardin_ Oct 09 2011