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A206616 Number of (n+1)X4 0..2 arrays with every 2X3 or 3X2 subblock having no more than two equal edges, and new values 0..2 introduced in row major order.

%I A206616 #7 Jul 22 2025 19:32:58
%S A206616 580,17708,623933,21744156,752689692,26135187233,907138039901,
%T A206616 31481198946322,1092605572922527,37920364043243138,
%U A206616 1316071917345653001,45675935634088583339,1585240798851880252784,55017771164461157130806
%N A206616 Number of (n+1)X4 0..2 arrays with every 2X3 or 3X2 subblock having no more than two equal edges, and new values 0..2 introduced in row major order.
%C A206616 Column 3 of A206621
%H A206616 R. H. Hardin, <a href="/A206616/b206616.txt">Table of n, a(n) for n = 1..210</a>
%F A206616 Empirical: a(n) = 37*a(n-1) -193*a(n-2) +4563*a(n-3) -26088*a(n-4) +213640*a(n-5) -2282905*a(n-6) +369531*a(n-7) +59365865*a(n-8) -119009270*a(n-9) -262257680*a(n-10) +527736231*a(n-11) +509956986*a(n-12) +4324710244*a(n-13) -23957378452*a(n-14) +23663119594*a(n-15) +61337666069*a(n-16) -218666604368*a(n-17) +228502952174*a(n-18) -85986086663*a(n-19) +669360026328*a(n-20) -249999620622*a(n-21) -2694789374595*a(n-22) +3166056347472*a(n-23) -4527450747937*a(n-24) +1962425462655*a(n-25) +11253630720214*a(n-26) -6950215731178*a(n-27) -8616642530280*a(n-28) +5352219023522*a(n-29) +18282316992761*a(n-30) +7753157593402*a(n-31) -40511908730324*a(n-32) +4939025872094*a(n-33) -60334135799883*a(n-34) +58664554195163*a(n-35) -121534792363268*a(n-36) +68593536567899*a(n-37) +27074083178241*a(n-38) +308051491547424*a(n-39) -39985515053935*a(n-40) +39295040533166*a(n-41) +83890931412882*a(n-42) -250291599920068*a(n-43) -288209619371358*a(n-44) -184438801479103*a(n-45) +38926434092468*a(n-46) -59238978126303*a(n-47) +106546892950000*a(n-48) +214149676500053*a(n-49) +116025062188772*a(n-50) -2859191597854*a(n-51) +39054500953935*a(n-52) -17011926676243*a(n-53) -44327153317680*a(n-54) -19261125626130*a(n-55) -3153801775828*a(n-56) -4604960888768*a(n-57) -7048617640872*a(n-58) -822479585408*a(n-59) +2623759339152*a(n-60) +177002043136*a(n-61) -414732129408*a(n-62) +52243793472*a(n-63) -4364697600*a(n-64) -4934155008*a(n-65) +884524032*a(n-66) -33288192*a(n-67)
%e A206616 Some solutions for n=4
%e A206616 ..0..0..0..0....0..0..1..2....0..1..2..1....0..0..1..2....0..1..0..2
%e A206616 ..1..2..1..2....0..1..0..0....1..0..1..2....2..1..2..2....1..2..2..1
%e A206616 ..1..0..0..0....2..0..2..1....0..1..1..2....1..0..0..1....1..0..1..2
%e A206616 ..1..2..1..2....1..0..2..0....0..2..0..1....1..2..1..2....0..1..2..0
%e A206616 ..2..1..0..2....0..1..0..1....1..2..1..2....2..0..2..0....0..2..0..0
%K A206616 nonn
%O A206616 1,1
%A A206616 _R. H. Hardin_ Feb 10 2012