|
%I #4 Aug 01 2018 13:47:09
%S 1,2,2,4,4,4,8,14,14,8,16,28,38,28,16,32,94,109,109,94,32,64,284,419,
%T 472,419,284,64,128,752,1413,2639,2639,1413,752,128,256,2244,4708,
%U 13134,23031,13134,4708,2244,256,512,6532,16406,64593,161091,161091,64593
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2.....4.......8.......16.........32..........64...........128
%C ...2....4....14......28.......94........284.........752..........2244
%C ...4...14....38.....109......419.......1413........4708.........16406
%C ...8...28...109.....472.....2639......13134.......64593........329236
%C ..16...94...419....2639....23031.....161091.....1160029.......8965243
%C ..32..284..1413...13134...161091....1624676....17100005.....193630364
%C ..64..752..4708...64593..1160029...17100005...271661553....4668181991
%C .128.2244.16406..329236..8965243..193630364..4668181991..124728567511
%C .256.6532.56424.1675126.67933591.2178634452.80648172452.3358612290228
%H R. H. Hardin, <a href="/A317611/b317611.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6
%F k=3: [order 15] for n>17
%F k=4: [order 61] for n>63
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..0..0..0. .0..0..0..0. .0..1..0..0. .0..0..0..0
%e ..0..1..0..1. .1..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..1
%e ..0..1..1..1. .0..0..1..0. .0..0..0..1. .0..0..0..0. .1..0..0..0
%e ..0..0..1..1. .0..0..0..1. .1..0..0..0. .0..0..0..1. .0..1..0..0
%e ..0..0..1..1. .0..0..0..0. .0..1..0..0. .0..0..0..1. .0..0..1..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A304341.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Aug 01 2018
| 