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A241054 T(n,k)=Number of nXk 0..3 arrays with no element equal to one 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

%I A241054 #6 Jun 02 2025 10:01:04
%S A241054 2,3,2,4,3,4,7,2,4,6,10,10,3,6,8,15,18,24,6,8,14,24,18,60,64,6,12,20,
%T A241054 35,46,93,163,132,15,13,30,54,58,297,280,598,690,31,20,48,83,102,507,
%U A241054 1423,1392,3411,2142,58,28,70,124,173,1264,4167,10921,13273,11283,7144,170,38
%N A241054 T(n,k)=Number of nXk 0..3 arrays with no element equal to one 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 or one plus the sum of the elements antidiagonally to its northeast, modulo 4.
%C A241054 Table starts
%C A241054 ..2..3...4.....7......10........15..........24..........35..........54
%C A241054 ..2..3...2....10......18........18..........46..........58.........102
%C A241054 ..4..4...3....24......60........93.........297.........507........1264
%C A241054 ..6..6...6....64.....163.......280........1423........4167.......13389
%C A241054 ..8..8...6...132.....598......1392.......10921.......72769......370453
%C A241054 .14.12..15...690....3411.....13273......189680.....2667280....18820225
%C A241054 .20.13..31..2142...11283.....89910.....1511923....30914092...376386754
%C A241054 .30.20..58..7144...72578...1128052....35582068..1432670661.26960360814
%C A241054 .48.28.170.30662..404421..13331118...776191453.62057946683
%C A241054 .70.38.388.95669.2220973.128026529.14877945554
%H A241054 R. H. Hardin, <a href="/A241054/b241054.txt">Table of n, a(n) for n = 1..143</a>
%F A241054 Empirical for column k:
%F A241054 k=1: a(n) = a(n-2) +2*a(n-3)
%F A241054 k=2: a(n) = 2*a(n-2) -a(n-4) +a(n-5) -a(n-7) +a(n-8) +a(n-11) for n>15
%F A241054 Empirical for row n:
%F A241054 n=1: a(n) = a(n-2) +2*a(n-3)
%F A241054 n=2: [order 15] for n>17
%F A241054 n=3: [order 70] for n>85
%e A241054 Some solutions for n=4 k=4
%e A241054 ..3..2..3..3....3..3..2..2....3..2..3..2....3..3..2..3....3..3..2..2
%e A241054 ..2..1..1..0....2..1..1..3....2..1..1..0....2..1..1..0....2..1..1..3
%e A241054 ..2..0..2..0....3..3..2..2....2..1..3..0....3..3..2..2....3..3..2..3
%e A241054 ..2..0..0..0....2..0..2..0....2..1..2..0....3..1..0..0....2..1..2..3
%Y A241054 Column 1 is A239851
%Y A241054 Row 1 is A159288(n+1)
%K A241054 nonn,tabl
%O A241054 1,1
%A A241054 _R. H. Hardin_, Apr 15 2014