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A240395 Number of 3 X n 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 two plus the sum of the elements diagonally to its northwest, modulo 4. 1

%I

%S 2,12,32,62,118,206,351,568,882,1322,1921,2716,3748,5062,6707,8736,

%T 11206,14178,17717,21892,26776,32446,38983,46472,55002,64666,75561,

%U 87788,101452,116662,133531,152176,172718,195282,219997,246996,276416,308398

%N Number of 3 X n 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 two plus the sum of the elements diagonally to its northwest, modulo 4.

%H R. H. Hardin, <a href="/A240395/b240395.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/6)*n^4 - (5/6)*n^3 + (13/3)*n^2 + (31/3)*n - 48 for n>5.

%F Conjectures from _Colin Barker_, Oct 27 2018: (Start)

%F G.f.: x*(2 + 2*x - 8*x^2 + 2*x^3 + 18*x^4 - 26*x^5 + 29*x^6 - 29*x^7 + 20*x^8 - 6*x^9) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>10.

%F (End)

%e Some solutions for n=4:

%e ..3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0

%e ..1..3..3..0....1..0..0..0....1..0..0..3....1..0..3..3....1..0..3..3

%e ..3..1..3..2....3..0..2..3....3..0..0..1....3..2..3..2....3..0..2..2

%Y Row 3 of A240394.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 04 2014

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Last modified September 24 21:51 EDT 2022. Contains 356949 sequences. (Running on oeis4.)