A204195 - OEIS

%I #6 Feb 22 2020 20:54:24

%S 13,338,639,2974,15780,85681,461894,2501104,13632039,74052393,

%T 402461304,2191865388,11921228286,64849845095,352971589737,

%U 1920427592045,10448975722238,56861941373875,309398162988521,1683518039170569

%N Number of nX6 0..1 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..1 introduced in row major order

%C Column 6 of A204197

%H R. H. Hardin, <a href="/A204195/b204195.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +31*a(n-2) +35*a(n-3) -484*a(n-4) -1540*a(n-5) +3777*a(n-6) +20893*a(n-7) -13095*a(n-8) -164056*a(n-9) -16952*a(n-10) +869315*a(n-11) +423945*a(n-12) -3331324*a(n-13) -2443045*a(n-14) +9580242*a(n-15) +8783514*a(n-16) -20921269*a(n-17) -22487170*a(n-18) +34029198*a(n-19) +42683153*a(n-20) -36702281*a(n-21) -60385183*a(n-22) +6484881*a(n-23) +60452592*a(n-24) +86335845*a(n-25) -28135499*a(n-26) -265626651*a(n-27) -47512120*a(n-28) +519637756*a(n-29) +167575352*a(n-30) -778001921*a(n-31) -307355299*a(n-32) +937958248*a(n-33) +413493468*a(n-34) -932671308*a(n-35) -436727605*a(n-36) +777199379*a(n-37) +371775387*a(n-38) -549109886*a(n-39) -258827566*a(n-40) +331294225*a(n-41) +148701189*a(n-42) -170956550*a(n-43) -70899421*a(n-44) +75122009*a(n-45) +28170567*a(n-46) -27830001*a(n-47) -9373320*a(n-48) +8563116*a(n-49) +2633996*a(n-50) -2146199*a(n-51) -633969*a(n-52) +427694*a(n-53) +132590*a(n-54) -65792*a(n-55) -23983*a(n-56) +7541*a(n-57) +3580*a(n-58) -618*a(n-59) -401*a(n-60) +34*a(n-61) +29*a(n-62) -a(n-63) -a(n-64) for n>67

%e Some solutions for n=5

%e ..0..1..0..0..1..1....0..1..1..0..0..1....0..1..0..1..1..0....0..0..1..1..0..1

%e ..1..0..1..1..0..0....0..1..0..1..1..0....0..1..0..1..0..1....0..1..0..0..1..0

%e ..0..0..1..0..0..1....1..0..1..1..0..1....1..0..1..0..1..1....1..0..1..1..0..0

%e ..1..1..0..1..1..0....1..0..1..0..0..1....0..1..1..0..1..0....0..1..1..0..1..1

%e ..1..1..0..1..0..1....0..1..0..1..1..0....1..1..0..1..0..1....1..1..0..0..1..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 12 2012