A249986 Number of length 6+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 6*n.

466, 7138, 43068, 168506, 508902, 1290856, 2886016, 5862924, 11046810, 19587334, 33034276, 53421174, 83356910, 126125244, 185792296, 267321976, 376699362, 521062026, 708839308, 949899538, 1255705206, 1639476080, 2116360272

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1987/180)*n^6 + (2033/30)*n^5 + (2785/18)*n^4 + 226*n^3 - (3017/180)*n^2 + (697/30)*n.

Conjectures from Colin Barker, Nov 10 2018: (Start)

G.f.: 2*x*(233 + 1938*x + 1444*x^2 + 309*x^3 + 134*x^4 - 84*x^5) / (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>7.

(End)

Example

Some solutions for n=4:
..5....0....0....5....2....4....2....5....2....0....0....3....0....0....1....5
..2....5....7....0....8....7....4....0....1....1....3....0....2....2....7....1
..0....0....1....6....6....1....0....7....7....6....6....8....7....0....2....5
..8....0....3....8....1....6....6....8....0....8....4....8....1....4....0....2
..0....4....4....8....5....0....0....5....3....2....8....1....3....6....0....5
..2....8....8....0....7....3....5....0....5....6....1....7....6....0....7....8
..3....2....4....3....2....2....4....3....0....0....6....7....0....8....3....1

Crossrefs

Row 6 of A249982.

Sequence in context: A069399 A145637 A051987 * A373135 A273808 A034593

Adjacent sequences: A249983 A249984 A249985 * A249987 A249988 A249989

Keyword

nonn

Author

R. H. Hardin, Nov 10 2014

Status

approved