A250859 Number of (7+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.

983950, 5480917, 20067117, 57570016, 140301126, 303858745, 601566177, 1109545432, 1932426406, 3209691541, 5122655965, 7902083112, 11836435822, 17280762921, 24666221281, 34510233360, 47427280222, 64140330037, 85492902061

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..23

Formula

Empirical: a(n) = (15887/18)*n^6 + (39464/3)*n^5 + (2674189/36)*n^4 + (462227/2)*n^3 + (12645859/36)*n^2 + (743119/3)*n + 65536.

Conjectures from Colin Barker, Nov 22 2018: (Start)

G.f.: x*(983950 - 1406733*x + 2363648*x^2 - 2238796*x^3 + 1326626*x^4 - 458751*x^5 + 65536*x^6) / (1 - x)^7.

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.

(End)

Example

Some solutions for n=1:
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..0....0..0....0..0....0..0....2..2....1..1....1..1....1..1....1..1....2..2
..3..3....2..3....2..2....2..2....0..0....2..2....0..0....2..3....0..0....0..0
..2..3....1..2....3..3....0..0....2..2....2..2....1..1....1..2....1..1....3..3
..2..3....1..2....2..2....1..3....0..1....2..2....1..1....1..2....0..0....1..2
..1..3....1..3....2..2....1..3....0..1....1..2....1..2....0..2....3..3....2..3
..0..2....1..3....0..0....1..3....0..1....2..3....2..3....1..3....1..1....1..2
..1..3....1..3....0..2....0..3....1..2....0..3....0..1....0..2....0..0....0..2

Crossrefs

Row 7 of A250853.

Sequence in context: A251471 A213125 A344038 * A251450 A205656 A206185

Adjacent sequences: A250856 A250857 A250858 * A250860 A250861 A250862

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved