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A241435 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or one 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 A241435 #6 Jun 02 2025 10:08:59
%S A241435 2,3,3,4,5,4,7,10,2,7,10,21,22,3,10,15,45,74,97,5,15,24,88,158,515,
%T A241435 213,6,24,35,181,448,1563,1527,381,9,35,54,378,1272,5915,7495,5304,
%U A241435 1005,10,54,83,710,3284,22712,45139,37148,20690,1900,15,83,124,1460,8331,76145
%N A241435 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or one 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 A241435 Table starts
%C A241435 ..2..3.....4......7.......10.........15..........24..........35..........54
%C A241435 ..3..5....10.....21.......45.........88.........181.........378.........710
%C A241435 ..4..2....22.....74......158........448........1272........3284........8331
%C A241435 ..7..3....97....515.....1563.......5915.......22712.......76145......270960
%C A241435 .10..5...213...1527.....7495......45139......282527.....1304136.....6927135
%C A241435 .15..6...381...5304....37148.....377314.....4122537....29425635...269064197
%C A241435 .24..9..1005..20690...218885....4136727....79901137..1058201862.16609740868
%C A241435 .35.10..1900..61348..1059975...34541924..1231102996.34796682706
%C A241435 .54.15..4137.257119..7257895..418453966.26880310825
%C A241435 .83.21.10518.920918.44141371.4088141292
%H A241435 R. H. Hardin, <a href="/A241435/b241435.txt">Table of n, a(n) for n = 1..126</a>
%F A241435 Empirical for column k:
%F A241435 k=1: a(n) = a(n-2) +2*a(n-3)
%F A241435 k=2: [order 11] for n>13
%F A241435 Empirical for row n:
%F A241435 n=1: a(n) = a(n-2) +2*a(n-3)
%F A241435 n=2: [order 22] for n>24
%e A241435 Some solutions for n=4 k=4
%e A241435 ..2..2..3..3....2..2..3..3....2..2..3..2....3..2..3..2....3..2..3..2
%e A241435 ..2..1..3..2....2..1..1..2....2..1..1..0....2..1..1..0....2..1..1..2
%e A241435 ..3..1..0..0....3..3..0..0....3..1..0..2....3..1..3..2....3..1..2..2
%e A241435 ..2..0..0..0....2..2..2..0....3..2..0..0....3..2..1..2....2..0..0..0
%Y A241435 Column and row 1 are A159288(n+1)
%K A241435 nonn,tabl
%O A241435 1,1
%A A241435 _R. H. Hardin_, Apr 22 2014