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A240460 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

%I A240460 #6 Jun 02 2025 09:58:50
%S A240460 2,4,5,8,21,12,16,89,102,28,32,375,874,476,66,64,1583,7589,8187,2200,
%T A240460 156,128,6685,65723,143237,75167,10123,368,256,28241,568370,2501883,
%U A240460 2632690,682018,46471,868,512,119319,4916340,43654661,92193017,47636104,6147372
%N A240460 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.
%C A240460 Table starts
%C A240460 ....2.......4..........8...........16............32.............64
%C A240460 ....5......21.........89..........375..........1583...........6685
%C A240460 ...12.....102........874.........7589.........65723.........568370
%C A240460 ...28.....476.......8187.......143237.......2501883.......43654661
%C A240460 ...66....2200......75167......2632690......92193017.....3228706651
%C A240460 ..156...10123.....682018.....47636104....3337483054...234122685500
%C A240460 ..368...46471....6147372....854671234..119643524281.16795323356869
%C A240460 ..868..213000...55212526..15259447330.4265146133201
%C A240460 .2048..975380..494809053.271656519692
%C A240460 .4832.4464474.4428808128
%H A240460 R. H. Hardin, <a href="/A240460/b240460.txt">Table of n, a(n) for n = 1..84</a>
%F A240460 Empirical for column k:
%F A240460 k=1: a(n) = 2*a(n-1) +2*a(n-3)
%F A240460 k=2: [order 26]
%F A240460 Empirical for row n:
%F A240460 n=1: a(n) = 2*a(n-1)
%F A240460 n=2: a(n) = 6*a(n-1) -7*a(n-2) -4*a(n-3) +8*a(n-4)
%F A240460 n=3: [order 23]
%e A240460 Some solutions for n=4 k=4
%e A240460 ..2..0..0..0....2..2..0..0....0..0..0..2....0..2..2..2....2..2..2..2
%e A240460 ..0..0..2..0....2..0..2..0....0..2..0..0....0..0..0..0....2..0..0..0
%e A240460 ..0..0..0..0....2..2..2..2....0..0..2..2....0..0..2..0....0..2..2..2
%e A240460 ..0..2..2..0....3..1..0..0....0..2..2..2....2..2..2..0....0..2..0..0
%Y A240460 Column 1 is A239333
%Y A240460 Row 1 is A000079
%K A240460 nonn,tabl
%O A240460 1,1
%A A240460 _R. H. Hardin_, Apr 05 2014