cp's OEIS Frontend

A301999 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

%I A301999 #4 Mar 30 2018 12:30:01
%S A301999 0,1,0,1,2,0,2,2,5,0,3,8,5,13,0,5,18,26,15,34,0,8,50,84,74,48,89,0,13,
%T A301999 128,309,468,200,155,233,0,21,338,1108,2036,2856,530,499,610,0,34,882,
%U A301999 3979,10982,14016,17800,1394,1602,1597,0,55,2312,14314,53440,122232
%N A301999 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
%C A301999 Table starts
%C A301999 .0....1....1....2.......3........5..........8..........13............21
%C A301999 .0....2....2....8......18.......50........128.........338...........882
%C A301999 .0....5....5...26......84......309.......1108........3979.........14314
%C A301999 .0...13...15...74.....468.....2036......10982.......53440........271596
%C A301999 .0...34...48..200....2856....14016.....122232......813704.......6066698
%C A301999 .0...89..155..530...17800...100176....1366374....12824770.....133115004
%C A301999 .0..233..499.1394..110036...729297...15243860...204666568....2933712940
%C A301999 .0..610.1602.3656..674984..5333386..169636124..3267873712...64653790404
%C A301999 .0.1597.5137.9578.4130664.39000114.1884309898.52110883753.1423142192108
%H A301999 R. H. Hardin, <a href="/A301999/b301999.txt">Table of n, a(n) for n = 1..311</a>
%F A301999 Empirical for column k:
%F A301999 k=1: a(n) = a(n-1)
%F A301999 k=2: a(n) = 3*a(n-1) -a(n-2)
%F A301999 k=3: a(n) = 5*a(n-1) -7*a(n-2) +4*a(n-3)
%F A301999 k=4: a(n) = 4*a(n-1) -4*a(n-2) +a(n-3)
%F A301999 k=5: [order 11] for n>12
%F A301999 k=6: [order 32] for n>33
%F A301999 k=7: [order 52] for n>54
%F A301999 Empirical for row n:
%F A301999 n=1: a(n) = a(n-1) +a(n-2)
%F A301999 n=2: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)
%F A301999 n=3: [order 20]
%e A301999 Some solutions for n=5 k=4
%e A301999 ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..0
%e A301999 ..1..1..0..1. .1..1..0..0. .0..0..0..0. .0..1..0..0. .0..1..0..0
%e A301999 ..1..0..1..0. .1..1..0..1. .1..1..1..1. .1..0..1..0. .1..1..0..0
%e A301999 ..0..1..0..1. .1..0..1..0. .0..0..1..0. .0..1..0..1. .1..1..1..1
%e A301999 ..0..0..1..1. .1..1..0..0. .0..1..0..0. .1..0..1..1. .0..0..1..1
%Y A301999 Column 2 is A001519.
%Y A301999 Row 1 is A000045(n-1).
%Y A301999 Row 2 is A175395(n-1).
%K A301999 nonn,tabl
%O A301999 1,5
%A A301999 _R. H. Hardin_, Mar 30 2018