cp's OEIS Frontend

A228754 T(n,k)=Number of nXk binary arrays with top left element equal to 1 and no two ones adjacent horizontally or antidiagonally.

%I A228754 #7 Sep 03 2013 23:52:40
%S A228754 1,1,2,2,3,4,3,9,8,8,5,20,39,21,16,8,50,126,168,55,32,13,119,482,780,
%T A228754 723,144,64,21,289,1712,4599,4808,3111,377,128,34,696,6277,24246,
%U A228754 43862,29608,13386,987,256,55,1682,22700,134440,342207,418370,182288,57597,2584,512
%N A228754 T(n,k)=Number of nXk binary arrays with top left element equal to 1 and no two ones adjacent horizontally or antidiagonally.
%C A228754 Table starts
%C A228754 ...1....1......2.......3.........5...........8...........13.............21
%C A228754 ...2....3......9......20........50.........119..........289............696
%C A228754 ...4....8.....39.....126.......482........1712.........6277..........22700
%C A228754 ...8...21....168.....780......4599.......24246.......134440.........728537
%C A228754 ..16...55....723....4808.....43862......342207......2876170.......23326164
%C A228754 ..32..144...3111...29608....418370.....4823826.....61534448......746135864
%C A228754 ..64..377..13386..182288...3990739....67970044...1316714732....23857469157
%C A228754 .128..987..57597.1122240..38067290...957616341..28177227352...762713002760
%C A228754 .256.2584.247827.6908896.363121586.13491214832.602998827928.24382157716612
%H A228754 R. H. Hardin, <a href="/A228754/b228754.txt">Table of n, a(n) for n = 1..1347</a>
%F A228754 Empirical for column k:
%F A228754 k=1: a(n) = 2*a(n-1)
%F A228754 k=2: a(n) = 3*a(n-1) -a(n-2)
%F A228754 k=3: a(n) = 5*a(n-1) -3*a(n-2)
%F A228754 k=4: a(n) = 8*a(n-1) -12*a(n-2) +4*a(n-3)
%F A228754 k=5: a(n) = 13*a(n-1) -36*a(n-2) +29*a(n-3) -5*a(n-4) for n>5
%F A228754 k=6: a(n) = 21*a(n-1) -112*a(n-2) +217*a(n-3) -157*a(n-4) +36*a(n-5) for n>6
%F A228754 k=7: [order 7] for n>9
%F A228754 Empirical for row n:
%F A228754 n=1: a(n) = a(n-1) +a(n-2)
%F A228754 n=2: a(n) = a(n-1) +3*a(n-2) +a(n-3)
%F A228754 n=3: a(n) = 2*a(n-1) +6*a(n-2) -a(n-4)
%F A228754 n=4: [order 8]
%F A228754 n=5: [order 13]
%F A228754 n=6: [order 21]
%F A228754 n=7: [order 34]
%e A228754 Some solutions for n=4 k=4
%e A228754 ..1..0..1..0....1..0..0..1....1..0..0..0....1..0..0..1....1..0..1..0
%e A228754 ..0..0..0..1....1..0..0..0....1..0..0..0....0..1..0..0....1..0..0..1
%e A228754 ..0..0..0..0....1..0..0..1....0..0..0..0....0..0..0..1....0..1..0..1
%e A228754 ..0..0..0..1....0..0..0..0....0..1..0..0....0..1..0..0....0..0..0..0
%Y A228754 Column 1 is A000079(n-1)
%Y A228754 Column 2 is A001906
%Y A228754 Column 3 is A095939
%Y A228754 Row 1 is A000045
%Y A228754 Row 2 is A097075(n+1)
%K A228754 nonn,tabl
%O A228754 1,3
%A A228754 _R. H. Hardin_ Sep 02 2013