A302415 - OEIS

%I #4 Apr 07 2018 17:03:28

%S 1,2,2,4,8,4,8,17,25,8,16,37,30,81,16,32,78,66,120,264,32,64,169,142,

%T 259,441,857,64,128,361,289,698,994,1431,2785,128,256,778,599,1650,

%U 3553,3548,4754,9050,256,512,1673,1268,3655,11998,16123,12442,16423,29407,512,1024

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ...1.....2.....4......8......16.......32........64........128.........256

%C ...2.....8....17.....37......78......169.......361........778........1673

%C ...4....25....30.....66.....142......289.......599.......1268........2660

%C ...8....81...120....259.....698.....1650......3655.......8544.......20246

%C ..16...264...441....994....3553....11998.....33596......98387......295578

%C ..32...857..1431...3548...16123....84581....306064....1137414.....4669030

%C ..64..2785..4754..12442...69537...518736...2342685...10963076....58365289

%C .128..9050.16423..46066..318944..3464956..20184979..119713006...845708279

%C .256.29407.55848.166341.1443006.23154338.170625048.1280996808.12137387233

%H R. H. Hardin, <a href="/A302415/b302415.txt">Table of n, a(n) for n = 1..288</a>

%F Empirical for column k:

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

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

%F k=3: [order 13]

%F k=4: [order 31] for n>33

%F k=5: [order 66] for n>73

%F Empirical for row n:

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

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

%F n=3: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -4*a(n-4) +a(n-5) for n>9

%F n=4: [order 16] for n>21

%F n=5: [order 31] for n>39

%F n=6: [order 79] for n>86

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A240478.

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

%Y Row 2 is A281470.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Apr 07 2018