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R. H. Hardin, <a href="/A280904/b280904.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of 3Xn 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 9, 646, 22568, 492490, 9426050, 162640161, 2636238543, 40818734359, 610807332682, 8899797476985, 126936297853576, 1779063560531884, 24572630681534366, 335222285940398228, 4524762545977409290

1,2

Row 3 of A280902.

Empirical: a(n) = 33*a(n-1) -294*a(n-2) -667*a(n-3) +16806*a(n-4) -5121*a(n-5) -389950*a(n-6) +278709*a(n-7) +5095965*a(n-8) -3346390*a(n-9) -41873331*a(n-10) +15827649*a(n-11) +225089912*a(n-12) +21687735*a(n-13) -781184967*a(n-14) -677069112*a(n-15) +1532218374*a(n-16) +3816125286*a(n-17) -205248782*a(n-18) -10810606968*a(n-19) -8772390618*a(n-20) +14265527040*a(n-21) +28972645413*a(n-22) +4449696537*a(n-23) -47676340890*a(n-24) -49006792749*a(n-25) +33750291246*a(n-26) +84325212377*a(n-27) +22629768081*a(n-28) -73666126236*a(n-29) -77116545584*a(n-30) +28481649930*a(n-31) +84486500724*a(n-32) +8922526848*a(n-33) -53642734755*a(n-34) -20170947015*a(n-35) +20632416015*a(n-36) +15610729314*a(n-37) -3175177428*a(n-38) -8006609696*a(n-39) -1561010208*a(n-40) +2779299648*a(n-41) +1314081664*a(n-42) -535991040*a(n-43) -521884416*a(n-44) -26788352*a(n-45) +145327104*a(n-46) +56180736*a(n-47) -25534464*a(n-48) -17252352*a(n-49) +688128*a(n-50) +2818048*a(n-51) +983040*a(n-52) -393216*a(n-53) -262144*a(n-54) for n>60

Some solutions for n=4

..0..1..1..1. .0..0..1..2. .0..1..1..0. .0..0..1..1. .0..1..0..0

..0..1..2..0. .2..2..2..0. .0..0..1..0. .1..0..0..1. .1..0..1..0

..1..0..1..1. .0..1..2..0. .0..1..1..2. .1..0..1..1. .1..2..0..0

Cf. A280902.

allocated

nonn

R. H. Hardin, Jan 10 2017

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