A250781 Number of (n+1) X (6+1) 0..1 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.

436, 1106, 2604, 5882, 12950, 27986, 59590, 125334, 260916, 538538, 1103752, 2249266, 4562698, 9222258, 18588322, 37386830, 75076376, 150582730, 301768276, 604371338, 1209885342, 2421317714, 4844708318, 9692167046, 19387949788

Offset

1,1

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 44*a(n-2) + 112*a(n-3) - 182*a(n-4) + 196*a(n-5) - 140*a(n-6) + 64*a(n-7) - 17*a(n-8) + 2*a(n-9).

Conjectures from Colin Barker, Nov 19 2018: (Start)

G.f.: 2*x*(218 - 1627*x + 5364*x^2 - 10163*x^3 + 12093*x^4 - 9259*x^5 + 4469*x^6 - 1253*x^7 + 160*x^8) / ((1 - x)^8*(1 - 2*x)).

a(n) = (2520*(289*2^n-209) - 314796*n - 41972*n^2 - 23779*n^3 + 385*n^4 - 364*n^5 + 7*n^6 - n^7) / 1260.

(End)

Example

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

Crossrefs

Column 6 of A250783.

Sequence in context: A345554 A345808 A260366 * A260012 A234221 A255777

Adjacent sequences: A250778 A250779 A250780 * A250782 A250783 A250784

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved