|
%I #4 Sep 23 2015 18:52:24
%S 1,1,2,1,3,4,1,6,9,7,1,11,36,17,13,1,22,121,115,37,26,1,43,484,457,
%T 469,107,52,1,86,1849,3055,2413,2622,321,103,1,171,7396,16081,30229,
%U 22907,15732,865,205,1,342,29241,107731,234421,552430,239281,85723,2449,410,1
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row divisible by 3 and each column divisible by 5, read as a binary number with top and left being the most significant bits.
%C Table starts
%C ...1....1.......1.........1...........1............1............1............1
%C ...2....3.......6........11..........22...........43...........86..........171
%C ...4....9......36.......121.........484.........1849.........7396........29241
%C ...7...17.....115.......457........3055........16081.......107731.......655001
%C ..13...37.....469......2413.......30229.......234421......2924245.....29005981
%C ..26..107....2622.....22907......552430......8080915....194647694...3858564731
%C ..52..321...15732....239281....11489332....326748241..15659602612.630055962801
%C .103..865...85723...2028469...198237391..10190636521.997197229531
%C .205.2449..494605..19072681..3805146805.367750753321
%C .410.7299.2942190.195594107.77803476910
%H R. H. Hardin, <a href="/A262472/b262472.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4)
%F k=2: [order 8]
%F k=3: [order 15]
%F k=4: [order 73]
%F Empirical for row n:
%F n=1: a(n) = a(n-1)
%F n=2: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)
%F n=3: a(n) = 4*a(n-1) +5*a(n-2) -20*a(n-3) -4*a(n-4) +16*a(n-5)
%F n=4: [order 13]
%F n=5: [order 33]
%F n=6: [order 67]
%e Some solutions for n=4 k=4
%e ..0..0..0..0..0....0..0..0..0..0....0..1..1..0..0....0..1..0..0..1
%e ..0..1..0..0..1....0..1..1..0..0....0..1..0..0..1....0..0..0..1..1
%e ..0..0..0..0..0....0..1..0..0..1....0..1..1..1..1....0..1..0..0..1
%e ..0..1..0..0..1....0..1..1..0..0....0..1..0..0..1....0..0..0..1..1
%e ..0..0..0..0..0....0..1..0..0..1....0..0..0..1..1....0..0..0..0..0
%Y Column 1 is A262267(n-1).
%Y Row 2 is A005578(n+1).
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Sep 23 2015
| 