A250728 Number of (n+1)X(7+1) 0..1 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

1302, 3173, 6257, 11377, 19887, 34069, 57397, 95231, 155263, 248537, 390263, 601256, 909242, 1350837, 1973466, 2838027, 4021571, 5620807, 7755707, 10574024, 14256002, 19020095, 25128978, 32896671, 42696063, 54967661, 70228855, 89084528

Offset

1,1

Comments

Column 7 of A250729

Links

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

Formula

Empirical: a(n) = 8*a(n-1) -27*a(n-2) +48*a(n-3) -42*a(n-4) +42*a(n-6) -48*a(n-7) +27*a(n-8) -8*a(n-9) +a(n-10) for n>17

Empirical for n mod 2 = 0: a(n) = (1/20160)*n^8 + (1/420)*n^7 + (71/1440)*n^6 + (71/120)*n^5 + (17767/2880)*n^4 + (1159/120)*n^3 + (533033/1680)*n^2 + (86336/105)*n - 5 for n>7

Empirical for n mod 2 = 1: a(n) = (1/20160)*n^8 + (1/420)*n^7 + (71/1440)*n^6 + (71/120)*n^5 + (17767/2880)*n^4 + (1159/120)*n^3 + (533033/1680)*n^2 + (86336/105)*n - 17 for n>7

Example

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

Crossrefs

Sequence in context: A022057 A107521 A226144 * A071847 A014356 A252308

Adjacent sequences: A250725 A250726 A250727 * A250729 A250730 A250731

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved