A316960 - OEIS

%I #4 Jul 17 2018 12:33:35

%S 1,2,2,4,8,4,8,32,32,8,16,128,220,128,16,32,512,1498,1498,512,32,64,

%T 2048,10243,16976,10243,2048,64,128,8192,70037,194917,194917,70037,

%U 8192,128,256,32768,478941,2232443,3796326,2232443,478941,32768,256,512,131072

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1......2........4..........8...........16.............32................64

%C ...2......8.......32........128..........512...........2048..............8192

%C ...4.....32......220.......1498........10243..........70037............478941

%C ...8....128.....1498......16976.......194917........2232443..........25592081

%C ..16....512....10243.....194917......3796326.......73529753........1426910760

%C ..32...2048....70037....2232443.....73529753.....2402722112.......78728223139

%C ..64...8192...478941...25592081...1426910760....78728223139.....4359094468163

%C .128..32768..3275421..293396247..27687032205..2579211359302...241311689147759

%C .256.131072.22400407.3363774685.537290478883.84510945441118.13360998189431905

%H R. H. Hardin, <a href="/A316960/b316960.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) = 4*a(n-1)

%F k=3: a(n) = 6*a(n-1) +9*a(n-2) -14*a(n-3) -52*a(n-4) -33*a(n-5) for n>6

%F k=4: [order 16] for n>17

%F k=5: [order 58] for n>59

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A004171(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 17 2018