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A301964 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

%I A301964 #4 Mar 29 2018 13:02:06
%S A301964 1,2,2,3,5,4,5,6,13,8,8,9,16,34,16,13,14,25,40,89,32,21,22,41,64,100,
%T A301964 233,64,34,35,74,111,169,252,610,128,55,56,132,219,311,441,632,1597,
%U A301964 256,89,90,239,443,749,874,1156,1588,4181,512,144,145,437,904,1803,2544,2454
%N A301964 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
%C A301964 Table starts
%C A301964 ...1....2....3....5.....8.....13.....21......34.......55........89.......144
%C A301964 ...2....5....6....9....14.....22.....35......56.......90.......145.......234
%C A301964 ...4...13...16...25....41.....74....132.....239......437.......800......1468
%C A301964 ...8...34...40...64...111....219....443.....904.....1860......3856......8015
%C A301964 ..16...89..100..169...311....749...1803....4257....10353.....25491.....62623
%C A301964 ..32..233..252..441...874...2544...7795...22456....66659....203926....621905
%C A301964 ..64..610..632.1156..2454...8705..33860..120603...444357...1715911...6574776
%C A301964 .128.1597.1588.3025..6906..29750.148299..655332..3014296..14863160..72345489
%C A301964 .256.4181.3988.7921.19427.101869.646838.3557239.20467528.129324707.802690313
%H A301964 R. H. Hardin, <a href="/A301964/b301964.txt">Table of n, a(n) for n = 1..880</a>
%F A301964 Empirical for column k:
%F A301964 k=1: a(n) = 2*a(n-1)
%F A301964 k=2: a(n) = 3*a(n-1) -a(n-2)
%F A301964 k=3: a(n) = a(n-1) +3*a(n-2) +2*a(n-3)
%F A301964 k=4: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3) for n>4
%F A301964 k=5: a(n) = 2*a(n-1) +3*a(n-2) -a(n-3) -2*a(n-4) -3*a(n-5) +2*a(n-6) for n>8
%F A301964 k=6: [order 11] for n>12
%F A301964 k=7: [order 14] for n>17
%F A301964 Empirical for row n:
%F A301964 n=1: a(n) = a(n-1) +a(n-2)
%F A301964 n=2: a(n) = 2*a(n-1) -a(n-3) for n>5
%F A301964 n=3: a(n) = 2*a(n-1) -a(n-4) for n>6
%F A301964 n=4: a(n) = 2*a(n-1) +a(n-3) -a(n-4) -2*a(n-6) +a(n-7) for n>9
%F A301964 n=5: [order 14] for n>17
%F A301964 n=6: [order 27] for n>32
%F A301964 n=7: [order 47] for n>52
%e A301964 Some solutions for n=5 k=4
%e A301964 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..0. .0..0..1..0
%e A301964 ..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..0..1..0. .1..1..1..0
%e A301964 ..0..0..0..1. .0..1..0..1. .0..1..0..1. .1..0..1..1. .1..0..1..0
%e A301964 ..0..1..1..1. .0..1..1..1. .1..0..1..0. .1..0..0..1. .0..1..0..1
%e A301964 ..0..1..0..1. .0..1..0..1. .1..0..1..1. .1..1..0..1. .0..1..0..1
%Y A301964 Column 1 is A000079(n-1).
%Y A301964 Column 2 is A001519(n+1).
%Y A301964 Row 1 is A000045(n+1).
%Y A301964 Row 2 is A301791.
%K A301964 nonn,tabl
%O A301964 1,2
%A A301964 _R. H. Hardin_, Mar 29 2018