cp's OEIS Frontend

A297314 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 or 2 neighboring 1s.

%I A297314 #4 Dec 28 2017 07:27:54
%S A297314 1,2,1,4,7,1,7,23,21,1,12,66,117,65,1,21,207,497,609,200,1,37,654,
%T A297314 2577,3808,3159,616,1,65,2049,13937,35476,29212,16389,1897,1,114,6422,
%U A297314 72541,340825,484808,223995,85041,5842,1,200,20119,375054,2997197,8273245
%N A297314 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 or 2 neighboring 1s.
%C A297314 Table starts
%C A297314 .1.....2.......4.........7..........12............21..............37
%C A297314 .1.....7......23........66.........207...........654............2049
%C A297314 .1....21.....117.......497........2577.........13937...........72541
%C A297314 .1....65.....609......3808.......35476........340825.........2997197
%C A297314 .1...200....3159.....29212......484808.......8273245.......121339476
%C A297314 .1...616...16389....223995.....6623719.....200646607......4893232934
%C A297314 .1..1897...85041...1717882....90535227....4869858862....197589351469
%C A297314 .1..5842..441225..13174266..1237278512..118156684121...7976248015498
%C A297314 .1.17991.2289339.101033369.16909630099.2867120332406.322003901582689
%H A297314 R. H. Hardin, <a href="/A297314/b297314.txt">Table of n, a(n) for n = 1..447</a>
%F A297314 Empirical for column k:
%F A297314 k=1: a(n) = a(n-1)
%F A297314 k=2: a(n) = 2*a(n-1) +3*a(n-2) +a(n-3)
%F A297314 k=3: a(n) = 3*a(n-1) +11*a(n-2) +3*a(n-3) -6*a(n-4)
%F A297314 k=4: [order 8] for n>9
%F A297314 k=5: [order 12] for n>14
%F A297314 k=6: [order 22] for n>25
%F A297314 k=7: [order 35] for n>39
%F A297314 Empirical for row n:
%F A297314 n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
%F A297314 n=2: [order 9]
%F A297314 n=3: [order 23]
%F A297314 n=4: [order 61]
%e A297314 Some solutions for n=5 k=4
%e A297314 ..0..1..1..1. .1..1..0..0. .1..1..1..0. .0..1..0..0. .0..0..1..0
%e A297314 ..1..0..0..0. .0..0..0..1. .0..0..1..0. .1..1..1..1. .1..1..0..0
%e A297314 ..0..1..0..1. .0..0..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..1
%e A297314 ..1..1..1..0. .0..0..1..0. .0..1..0..0. .0..0..1..1. .0..1..1..0
%e A297314 ..0..0..0..0. .0..1..1..1. .0..1..1..1. .0..0..1..1. .1..0..1..1
%Y A297314 Column 2 is A218836.
%Y A297314 Row 1 is A005251(n+2).
%K A297314 nonn,tabl
%O A297314 1,2
%A A297314 _R. H. Hardin_, Dec 28 2017