cp's OEIS Frontend

A240039 T(n,k)=Number of nXk 0..2 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest, modulo 3.

%I A240039 #6 Jun 02 2025 09:38:35
%S A240039 2,2,2,4,2,4,4,6,6,4,8,4,16,4,8,8,10,16,16,10,8,16,8,42,18,42,8,16,16,
%T A240039 20,44,52,52,44,20,16,32,16,114,62,154,62,114,16,32,32,40,122,162,178,
%U A240039 178,162,122,40,32,64,32,314,204,494,282,494,204,314,32,64,64,80,340,530,600
%N A240039 T(n,k)=Number of nXk 0..2 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest, modulo 3.
%C A240039 Table starts
%C A240039 ..2..2...4...4....8....8....16....16....32.....32.....64.....64.....128.....128
%C A240039 ..2..2...6...4...10....8....20....16....40.....32.....80.....64.....160.....128
%C A240039 ..4..6..16..16...42...44...114...122...314....340....872....950....2432....2658
%C A240039 ..4..4..16..18...52...62...162...204...530....672...1736...2198....5706....7202
%C A240039 ..8.10..42..52..154..178...494...600..1606...2014...5262...6690...17464...22360
%C A240039 ..8..8..44..62..178..282...710..1074..2770...4162..10836..15764...41374...59680
%C A240039 .16.20.114.162..494..710..1976..2884..7958..12074..31824..49078..130758..197208
%C A240039 .16.16.122.204..600.1074..2884..5706.14686..25224..66774.113794..307698..508002
%C A240039 .32.40.314.530.1606.2770..7958.14686.42470..72446.200916.360716..984770.1730698
%C A240039 .32.32.340.672.2014.4162.12074.25224.72446.147092.407954.778294.2194512.4046228
%H A240039 R. H. Hardin, <a href="/A240039/b240039.txt">Table of n, a(n) for n = 1..511</a>
%F A240039 Empirical for column k:
%F A240039 k=1: a(n) = 2*a(n-2)
%F A240039 k=2: a(n) = 2*a(n-2) for n>5
%F A240039 k=3: a(n) = 4*a(n-2) -3*a(n-4) -a(n-6) for n>7
%F A240039 k=4: [order 24] for n>27
%F A240039 k=5: [order 86] for n>89
%e A240039 Some solutions for n=3 k=4
%e A240039 ..2..1..1..2....2..1..2..1....2..1..2..1....1..2..1..2....1..2..1..2
%e A240039 ..1..0..0..0....1..0..0..0....1..0..0..0....2..0..0..0....2..0..0..0
%e A240039 ..1..0..0..0....1..0..0..0....2..0..0..0....2..0..0..0....2..0..0..1
%Y A240039 Column 1 is A016116(n+1)
%Y A240039 Column 2 is A163888(n-2) for n>3
%K A240039 nonn,tabl
%O A240039 1,1
%A A240039 _R. H. Hardin_, Mar 31 2014