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A231415 Number of (n+1)X(3+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

%I A231415 #6 Jul 23 2025 06:28:21
%S A231415 514,20896,844061,34099824,1378646988,55743171795,2253925687328,
%T A231415 91135639532050,3684995866308397,148999828418108116,
%U A231415 6024687611678499118,243603373370750396584,9849905481191885220441,398272965802692213756388
%N A231415 Number of (n+1)X(3+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.
%C A231415 Column 3 of A231419
%H A231415 R. H. Hardin, <a href="/A231415/b231415.txt">Table of n, a(n) for n = 1..210</a>
%F A231415 Empirical: a(n) = 46*a(n-1) -196*a(n-2) -1267*a(n-3) +3292*a(n-4) +14529*a(n-5) +171276*a(n-6) -1140184*a(n-7) -4475862*a(n-8) +10969543*a(n-9) +62966783*a(n-10) +91108201*a(n-11) +282085660*a(n-12) +647957840*a(n-13) -2319416710*a(n-14) -7818927246*a(n-15) -4993117801*a(n-16) +1684239825*a(n-17) +21907839370*a(n-18) +51944554645*a(n-19) +32558644866*a(n-20) -56438925441*a(n-21) -129903082195*a(n-22) -6021907645*a(n-23) -46647268966*a(n-24) +81404415386*a(n-25) +152792965116*a(n-26) -57732537680*a(n-27) +39345285424*a(n-28) -41777158208*a(n-29) -29468075264*a(n-30) +16816004096*a(n-31) +1488514048*a(n-32) -205930496*a(n-33) -244383744*a(n-34)
%e A231415 Some solutions for n=2
%e A231415 ..0..1..2..1....0..0..0..1....0..1..2..1....0..1..1..0....0..1..1..2
%e A231415 ..2..2..0..2....2..2..2..2....2..2..2..1....2..1..0..2....2..2..0..1
%e A231415 ..2..1..1..1....2..0..0..0....1..1..1..2....2..2..0..2....2..1..2..0
%K A231415 nonn
%O A231415 1,1
%A A231415 _R. H. Hardin_, Nov 08 2013