A317764 - OEIS

%I #4 Aug 06 2018 11:52:19

%S 1,2,2,4,6,4,8,10,10,8,16,20,16,20,16,32,42,28,28,42,32,64,89,52,43,

%T 52,89,64,128,190,100,72,72,100,190,128,256,407,196,127,109,127,196,

%U 407,256,512,873,388,232,177,177,232,388,873,512,1024,1874,772,432,302,266,302

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ...1...2...4...8..16...32...64..128..256..512.1024..2048..4096..8192.16384

%C ...2...6..10..20..42...89..190..407..873.1874.4024..8642.18561.39866.85627

%C ...4..10..16..28..52..100..196..388..772.1540.3076..6148.12292.24580.49156

%C ...8..20..28..43..72..127..232..432..813.1539.2922..5557.10577.20141.38362

%C ..16..42..52..72.109..177..302..532..955.1733.3164..5796.10637.19541.35918

%C ..32..89.100.127.177..266..425..709.1217.2126.3753..6666.11882.21223.37952

%C ..64.190.196.232.302..425..639.1012.1663.2801.4792..8278.14385.25088.43852

%C .128.407.388.432.532..709.1012.1529.2413.3927.6524.10984.18651.31842.54552

%C .256.873.772.813.955.1217.1663.2413.3674.5798.9381.15434.25672.43007.72386

%H R. H. Hardin, <a href="/A317764/b317764.txt">Table of n, a(n) for n = 1..1300</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

%F k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -a(n-4) for n>6

%F k=3: a(n) = 3*a(n-1) -2*a(n-2) for n>3

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

%F k=5: a(n) = 2*a(n-1) -a(n-4) for n>6

%F k=6: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) +a(n-7) for n>10

%F k=7: a(n) = 3*a(n-1) -2*a(n-2) -a(n-4) +a(n-5) -a(n-6) +a(n-7) for n>11

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 3 is A003461 for n>1.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Aug 06 2018