A220031 Number of n X 7 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 n X 7 array.

7, 18, 55, 137, 302, 613, 1165, 2094, 3587, 5893, 9335, 14323, 21368, 31097, 44269, 61792, 84741, 114377, 152167, 199805, 259234, 332669, 422621, 531922, 663751, 821661, 1009607, 1231975, 1493612, 1799857, 2156573, 2570180, 3047689, 3596737

Offset

1,1

Comments

Column 7 of A220032.

Links

R. H. Hardin, Table of n, a(n) for n = 1..68

Formula

Empirical: a(n) = (1/720)*n^6 + (7/240)*n^5 + (11/144)*n^4 + (25/48)*n^3 + (263/90)*n^2 + (29/20)*n - 4 for n>2.

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

G.f.: x*(7 - 31*x + 76*x^2 - 115*x^3 + 113*x^4 - 66*x^5 + 17*x^6 + x^7 - x^8) / (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>9.

(End)

Example

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

Crossrefs

Cf. A220032.

Sequence in context: A324944 A084819 A346494 * A197092 A288743 A223240

Adjacent sequences: A220028 A220029 A220030 * A220032 A220033 A220034

Keyword

nonn

Author

R. H. Hardin, Dec 03 2012

Status

approved