A281883 - OEIS

A281883

Number of n X 3 0..1 arrays with no element equal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%I #7 Jan 01 2024 01:21:52

%S 0,0,68,638,4832,35002,241209,1612568,10566034,68136376,433938423,

%T 2736019588,17108229189,106234294380,655764472080,4027264205666,

%U 24622851384305,149957156910166,910104036599313,5506462499669112

%N Number of n X 3 0..1 arrays with no element equal to more than four of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Column 3 of A281888.

%H R. H. Hardin, <a href="/A281883/b281883.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) -17*a(n-2) -28*a(n-3) -122*a(n-4) +132*a(n-5) +368*a(n-6) +570*a(n-7) +171*a(n-8) -746*a(n-9) -979*a(n-10) -2038*a(n-11) -1625*a(n-12) -840*a(n-13) -784*a(n-14) for n>17.

%e Some solutions for n=4

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

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

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

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

%Y Cf. A281888.

%K nonn

%O 1,3

%A _R. H. Hardin_, Feb 01 2017