|
%I #6 Sep 05 2022 10:54:43
%S 8,3,47,7,111,80,424,1157,2922,12816,33744,135689,427777,1511455,
%T 5237154,17740921,62498339,212645123,742064542,2553096441,8837428284,
%U 30568037684,105553660977,365371090457,1262061403870,4365797662037,15090331846613
%N Number of 4 X n 0..1 arrays with every element equal to 0, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C Row 4 of A302212.
%H R. H. Hardin, <a href="/A302214/b302214.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +28*a(n-2) -75*a(n-3) -398*a(n-4) +944*a(n-5) +3671*a(n-6) -7801*a(n-7) -24404*a(n-8) +47157*a(n-9) +124314*a(n-10) -221250*a(n-11) -505072*a(n-12) +836021*a(n-13) +1682425*a(n-14) -2608659*a(n-15) -4685786*a(n-16) +6844286*a(n-17) +11070045*a(n-18) -15306994*a(n-19) -22430872*a(n-20) +29493917*a(n-21) +39338431*a(n-22) -49375246*a(n-23) -60198503*a(n-24) +72293436*a(n-25) +81026935*a(n-26) -93046725*a(n-27) -96757097*a(n-28) +105632449*a(n-29) +103479364*a(n-30) -105909396*a(n-31) -100071471*a(n-32) +93611720*a(n-33) +88175650*a(n-34) -72499336*a(n-35) -70968961*a(n-36) +48606972*a(n-37) +51927035*a(n-38) -27622887*a(n-39) -34122752*a(n-40) +12814022*a(n-41) +19781216*a(n-42) -4480833*a(n-43) -9897585*a(n-44) +908537*a(n-45) +4168950*a(n-46) +107884*a(n-47) -1437073*a(n-48) -181920*a(n-49) +392409*a(n-50) +83213*a(n-51) -81617*a(n-52) -23241*a(n-53) +12292*a(n-54) +4271*a(n-55) -1246*a(n-56) -502*a(n-57) +75*a(n-58) +34*a(n-59) -2*a(n-60) -a(n-61) for n>62.
%e Some solutions for n=5
%e ..0..1..1..0..0. .0..1..0..0..1. .0..0..1..0..0. .0..0..1..1..0
%e ..1..1..1..0..0. .0..1..0..0..1. .0..0..1..0..0. .0..0..0..1..1
%e ..0..1..0..0..1. .0..1..0..0..1. .1..1..0..1..1. .1..0..1..1..0
%e ..0..1..0..0..1. .1..1..1..0..0. .1..1..0..1..1. .1..0..1..1..0
%Y Cf. A302212.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 03 2018
|
