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 A240002 Number of 3 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4. 1

%I

%S 12,61,190,526,1262,2766,5647,10878,19971,35180,59780,98414,157524,

%T 245879,375214,560995,823326,1188015,1687817,2363873,3267365,4461408,

%U 6023201,8046460,10644157,13951590,18129810,23369432,29894858,37968941

%N Number of 3 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

%H R. H. Hardin, <a href="/A240002/b240002.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/40320)*n^8 + (1/2016)*n^7 + (7/576)*n^6 + (17/360)*n^5 + (6367/5760)*n^4 - (935/288)*n^3 + (28145/672)*n^2 - (114913/840)*n + 237 for n>6.

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

%F G.f.: x*(12 - 47*x + 73*x^2 + 4*x^3 - 244*x^4 + 558*x^5 - 737*x^6 + 651*x^7 - 375*x^8 + 86*x^9 + 91*x^10 - 128*x^11 + 80*x^12 - 27*x^13 + 4*x^14) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>15.

%F (End)

%e Some solutions for n=5:

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

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

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

%Y Row 3 of A240000.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 30 2014

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)