A249984 Number of length 4+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 4*n.

64, 384, 1242, 3030, 6252, 11524, 19574, 31242, 47480, 69352, 98034, 134814, 181092, 238380, 308302, 392594, 493104, 611792, 750730, 912102, 1098204, 1311444, 1554342, 1829530, 2139752, 2487864, 2876834, 3309742, 3789780, 4320252, 4904574

Offset

1,1

Links

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

Formula

Empirical: a(n) = (14/3)*n^4 + (56/3)*n^3 + (121/3)*n^2 - (5/3)*n + 2.

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

G.f.: 2*x*(32 + 32*x - 19*x^2 + 10*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

Some solutions for n=6:
..3...12....2....1....6....9...12....2....8...12....3....2...11...12....2....2
..0....0....9...11....2....3....2...11....0....6...11....6...12....1...12....9
.12....6....1....8...10....8...10....9....9...11....0...12....0....7....3....1
.10....6....1....0....5....2....6...11....3....0....1....5....4....2....7....3
..3....0...10....3...12....9....8....0....4....2....5...12...11....0....6...10

Crossrefs

Row 4 of A249982.

Sequence in context: A297343 A228759 A220976 * A221598 A017618 A343724

Adjacent sequences: A249981 A249982 A249983 * A249985 A249986 A249987

Keyword

nonn

Author

R. H. Hardin, Nov 10 2014

Status

approved