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Number of n X 2 0..5 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.
1

%I #9 Jun 14 2014 16:26:55

%S 15,30,5,135,282,51,848,1189,120,2596,3978,473,7680,9594,836,16302,

%T 22017,2208,35248,41604,3380,62174,78404,7167,113125,129100,10067,

%U 178415,215500,18583,291000,324765,24652,425790,499302,41363,643958,707364

%N Number of n X 2 0..5 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

%C Column 2 of A201142.

%H R. H. Hardin, <a href="/A201136/b201136.txt">Table of n, a(n) for n = 1..183</a>

%F Empirical: a(n) = a(n-3) +5*a(n-6) -5*a(n-9) -10*a(n-12) +10*a(n-15) +10*a(n-18) -10*a(n-21) -5*a(n-24) +5*a(n-27) +a(n-30) -a(n-33)

%F Subsequences for n modulo 6 = 1,2,3,4,5,0

%F p=(n+5)/6: a(n) = 44*p^5 - (251/6)*p^4 + (29/2)*p^3 - (5/3)*p^2

%F q=(n+4)/6: a(n) = 44*q^5 - (53/4)*q^4 - 1*q^3 + (1/4)*q^2

%F r=(n+3)/6: a(n) = (44/15)*r^5 + (4/3)*r^4 + (1/2)*r^3 + (1/6)*r^2 + (1/15)*r

%F s=(n+2)/6: a(n) = 44*s^5 + (721/12)*s^4 + 26*s^3 + (53/12)*s^2 + (1/2)*s

%F t=(n+1)/6: a(n) = 44*t^5 + (629/6)*t^4 + (185/2)*t^3 + (107/3)*t^2 + 5*t

%F u=(n+0)/6: a(n) = (44/15)*u^5 + (133/12)*u^4 + 17*u^3 + (161/12)*u^2 + (167/30)*u + 1.

%e Some solutions for n=10:

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

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

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

%e ..1..4....1..3....1..3....0..3....1..3....0..2....1..2....1..3....0..3....1..3

%e ..1..4....1..3....1..3....1..4....2..3....1..2....1..3....1..3....1..3....1..3

%e ..1..4....2..4....2..3....1..4....2..3....1..3....3..3....1..3....1..4....2..4

%e ..2..5....2..4....2..4....1..5....2..4....3..4....4..5....2..4....1..4....2..4

%e ..2..5....3..5....3..4....2..5....3..4....3..5....4..5....3..4....2..5....2..4

%e ..2..5....4..5....4..5....2..5....4..5....4..5....4..5....4..5....2..5....2..5

%e ..2..5....4..5....5..5....4..5....5..5....4..5....4..5....5..5....4..5....5..5

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2011