|
%I #4 Jan 12 2018 08:59:47
%S 0,2,3,10,28,76,213,645,1852,5642,17016,51810,158290,484347,1484262,
%T 4552873,13976949,42918852,131843755,405082273,1244758709,3825355448,
%U 11756644688,36133929611,111060564589,341360933527,1049237831619
%N Number of nX4 0..1 arrays with every element equal to 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.
%C Column 4 of A298087.
%H R. H. Hardin, <a href="/A298083/b298083.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) -4*a(n-2) -28*a(n-4) +10*a(n-5) +35*a(n-6) +103*a(n-7) -31*a(n-8) +31*a(n-9) -383*a(n-10) +291*a(n-11) -598*a(n-12) -88*a(n-13) +16*a(n-14) -165*a(n-15) +1777*a(n-16) +1139*a(n-17) +1984*a(n-18) -2265*a(n-19) +1513*a(n-20) -2214*a(n-21) +6466*a(n-22) -9351*a(n-23) -128*a(n-24) -14148*a(n-25) -9460*a(n-26) -16824*a(n-27) +19925*a(n-28) +22443*a(n-29) +20906*a(n-30) +7763*a(n-31) +5741*a(n-32) -10077*a(n-33) +2720*a(n-34) +13550*a(n-35) -7017*a(n-36) -31393*a(n-37) -21978*a(n-38) +5034*a(n-39) +16547*a(n-40) +7238*a(n-41) -404*a(n-42) -6332*a(n-43) -2417*a(n-44) -5112*a(n-45) -816*a(n-46) -1724*a(n-47) +1953*a(n-48) +1176*a(n-49) +1643*a(n-50) -112*a(n-51) -110*a(n-52) -388*a(n-53) +15*a(n-54) -40*a(n-55) +26*a(n-56) +6*a(n-57) for n>58
%e Some solutions for n=7
%e ..0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1
%e ..0..0..1..1. .0..1..0..1. .0..1..1..0. .0..1..1..0. .0..1..0..1
%e ..1..1..1..1. .0..1..0..1. .1..1..0..1. .1..0..1..0. .0..1..0..1
%e ..1..0..1..1. .1..0..0..1. .0..0..0..1. .1..0..1..0. .0..0..1..1
%e ..0..1..0..0. .0..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1
%e ..0..1..0..1. .0..1..0..1. .0..1..1..0. .1..0..0..1. .1..0..0..1
%e ..0..0..1..1. .0..0..1..1. .0..0..0..0. .1..1..1..1. .1..1..1..1
%Y Cf. A298087.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 12 2018
| 