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A240192 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

%I A240192 #6 Jun 02 2025 09:41:54
%S A240192 1,1,2,1,5,3,1,8,12,4,1,14,37,27,7,1,26,129,138,73,10,1,50,478,771,
%T A240192 680,154,15,1,98,1908,5240,7170,2413,358,24,1,194,7868,40765,91879,
%U A240192 44594,10017,872,35,1,386,32888,336257,1399773,1005029,333607,43956,1871,54,1
%N A240192 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.
%C A240192 Table starts
%C A240192 ..1....1......1.........1...........1............1.............1.............1
%C A240192 ..2....5......8........14..........26...........50............98...........194
%C A240192 ..3...12.....37.......129.........478.........1908..........7868.........32888
%C A240192 ..4...27....138.......771........5240........40765........336257.......2843914
%C A240192 ..7...73....680......7170.......91879......1399773......22849697.....385366572
%C A240192 .10..154...2413.....44594.....1005029.....28061567.....865984451...28244997476
%C A240192 .15..358..10017....333607....14022582....733907809...43398047802.2752449791995
%C A240192 .24..872..43956...2715035...206345434..19388521135.2070573220929
%C A240192 .35.1871.159668..17332017..2336659626.394134037392
%C A240192 .54.4438.681760.134735700.33576330306
%H A240192 R. H. Hardin, <a href="/A240192/b240192.txt">Table of n, a(n) for n = 1..112</a>
%F A240192 Empirical for column k:
%F A240192 k=1: a(n) = a(n-2) +2*a(n-3)
%F A240192 k=2: [order 13]
%F A240192 Empirical for row n:
%F A240192 n=1: a(n) = a(n-1)
%F A240192 n=2: a(n) = 3*a(n-1) -2*a(n-2) for n>3
%F A240192 n=3: a(n) = 9*a(n-1) -27*a(n-2) +29*a(n-3) +6*a(n-4) -32*a(n-5) +16*a(n-6) for n>9
%F A240192 n=4: [order 29] for n>34
%e A240192 Some solutions for n=4 k=4
%e A240192 ..2..0..0..0....2..0..0..0....2..0..0..0....2..0..0..0....2..0..0..0
%e A240192 ..1..2..0..0....2..3..0..2....2..0..0..0....2..0..0..0....2..0..0..0
%e A240192 ..2..1..0..2....2..3..3..1....2..0..3..0....2..3..0..2....2..0..3..2
%e A240192 ..1..3..2..0....1..2..1..1....2..0..3..3....1..2..2..0....1..0..2..1
%Y A240192 Column 1 is A159288
%Y A240192 Row 2 is A164094(n-2)
%K A240192 nonn,tabl
%O A240192 1,3
%A A240192 _R. H. Hardin_, Apr 02 2014