A220037 Number of 7 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 7 X n array.

8, 14, 36, 119, 297, 626, 1165, 1963, 3088, 4630, 6711, 9492, 13175, 18010, 24304, 32431, 42843, 56082, 72793, 93738, 119811, 152054, 191674, 240061, 298807, 369726, 454875, 556576, 677439, 820386, 988676, 1185931, 1416163, 1683802, 1993725

Offset

1,1

Comments

Row 7 of A220032.

Links

R. H. Hardin, Table of n, a(n) for n = 1..53

Formula

Empirical: a(n) = (1/720)*n^6 - (7/240)*n^5 + (107/144)*n^4 - (209/48)*n^3 + (1609/45)*n^2 + (1913/60)*n - 813 for n>9.

Conjectures from Colin Barker, Jul 30 2018: (Start)

G.f.: x*(8 - 42*x + 106*x^2 - 119*x^3 + 10*x^4 + 108*x^5 - 123*x^6 + 58*x^7 + 36*x^8 - 68*x^9 + 33*x^10 - 10*x^11 - 2*x^12 + 10*x^13 - 3*x^14 - x^15) / (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>16.

(End)

Example

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

Crossrefs

Cf. A220032.

Sequence in context: A117132 A064969 A236332 * A144840 A257709 A121866

Adjacent sequences: A220034 A220035 A220036 * A220038 A220039 A220040

Keyword

nonn

Author

R. H. Hardin, Dec 03 2012

Status

approved