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A250856 Number of (4+1) X (n+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction. 1

%I

%S 12311,63631,223933,626416,1499679,3204951,6279401,11485528,19866631,

%T 32808359,52106341,80039896,119451823,173834271,247420689,345283856,

%U 473439991,638958943,850080461,1116336544,1448679871,1859618311

%N Number of (4+1) X (n+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

%H R. H. Hardin, <a href="/A250856/b250856.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (76/9)*n^6 + (1595/12)*n^5 + (28765/36)*n^4 + (31373/12)*n^3 + (155683/36)*n^2 + (10223/3)*n + 1024.

%F Conjectures from _Colin Barker_, Nov 21 2018: (Start)

%F G.f.: x*(12311 - 22546*x + 37047*x^2 - 35749*x^3 + 21160*x^4 - 7167*x^5 + 1024*x^6) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

%F (End)

%e Some solutions for n=2:

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

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

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

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

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

%Y Row 4 of A250853.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014

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Last modified January 23 10:36 EST 2020. Contains 331171 sequences. (Running on oeis4.)