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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 #8 Oct 27 2018 06:21:35

%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 March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)