A250895 Number of (n+1) X (5+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

3673, 11029, 33821, 102789, 305429, 890199, 2553537, 7243359, 20421217, 57483879, 162149489, 459536607, 1310548497, 3763833639, 10886111617, 31695302463, 92829953729, 273267490599, 807835524561, 2396325815007, 7127717418673

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 12*a(n-1) - 60*a(n-2) + 162*a(n-3) - 255*a(n-4) + 234*a(n-5) - 116*a(n-6) + 24*a(n-7) for n>9.

Conjectures from Colin Barker, Nov 23 2018: (Start)

G.f.: x*(3673 - 33047*x + 121853*x^2 - 236349*x^3 + 251138*x^4 - 133698*x^5 + 14708*x^6 + 21650*x^7 - 8800*x^8) / ((1 - x)^3*(1 - 2*x)^3*(1 - 3*x)).

a(n) = -877 + 1553*2^(-3+n) + 17956*3^(-3+n) + (976-2779*2^(-4+n))*n + (282+3087*2^(-4+n))*n^2 for n>2.

(End)

Example

Some solutions for n=4:
..2..1..1..0..0..0....1..1..0..0..0..0....0..1..1..0..0..1....2..1..1..1..0..0
..2..1..1..0..0..0....2..2..1..2..2..2....0..1..1..0..0..1....2..1..1..1..0..0
..2..2..2..1..1..1....1..1..0..1..1..1....1..2..2..1..1..2....2..1..1..1..0..1
..1..1..1..0..0..0....1..2..1..2..2..2....1..2..2..1..1..2....2..1..1..1..0..1
..1..1..1..1..1..2....0..1..0..1..1..1....0..1..1..0..0..1....1..0..0..2..1..2

Crossrefs

Column 5 of A250898.

Sequence in context: A283202 A365612 A205821 * A216139 A250702 A307890

Adjacent sequences: A250892 A250893 A250894 * A250896 A250897 A250898

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved