A252179 Number of length 3+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

12, 83, 264, 687, 1428, 2729, 4680, 7661, 11764, 17535, 25056, 35067, 47628, 63701, 83312, 107673, 136764, 172075, 213528, 262919, 320100, 387201, 463992, 552965, 653796, 769367, 899248, 1046739, 1211292, 1396653, 1602144, 1831985, 2085356

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 8*a(n-3) + 6*a(n-4) + 6*a(n-5) - 8*a(n-6) + 3*a(n-8) - a(n-9).

Empirical for n mod 2 = 0: a(n) = (1/60)*n^5 + (17/16)*n^4 + (14/3)*n^3 + (11/2)*n^2 + (77/30)*n + 1.

Empirical for n mod 2 = 1: a(n) = (1/60)*n^5 + (17/16)*n^4 + (14/3)*n^3 + (39/8)*n^2 + (79/60)*n + (1/16).

Empirical g.f.: x*(12 + 47*x + 15*x^2 - 9*x^3 - 41*x^4 - 13*x^5 + 3*x^6 + 3*x^7 - x^8) / ((1 - x)^6*(1 + x)^3). - Colin Barker, Dec 01 2018

Example

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

Crossrefs

Row 3 of A252177.

Sequence in context: A239180 A290715 A175037 * A102105 A275743 A026949

Adjacent sequences: A252176 A252177 A252178 * A252180 A252181 A252182

Keyword

nonn

Author

R. H. Hardin, Dec 15 2014

Status

approved