A248449 Number of length 1+5 0..n arrays with no three disjoint pairs in any consecutive six terms having the same sum.

42, 546, 3372, 13500, 41670, 107502, 243576, 499992, 949890, 1695450, 2874852, 4669716, 7313502, 11100390, 16395120, 23643312, 33382746, 46255122, 63018780, 84561900, 111916662, 146273886, 188998632, 241646280, 305979570, 383986122

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 14*a(n-2) + 14*a(n-3) - 14*a(n-5) + 14*a(n-6) - 6*a(n-7) + a(n-8).

Empirical for n mod 2 = 0: a(n) = n^6 + 6*n^5 + (15/2)*n^4 + 20*n^3 + 5*n^2 - 5*n.

Empirical for n mod 2 = 1: a(n) = n^6 + 6*n^5 + (15/2)*n^4 + 20*n^3 + 5*n^2 - 5*n + (15/2).

Empirical g.f.: 6*x*(7 + 49*x + 114*x^2 + 54*x^3 + 39*x^4 - 23*x^5) / ((1 - x)^7*(1 + x)). - Colin Barker, Nov 08 2018

Example

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

Crossrefs

Row 1 of A248448.

Sequence in context: A160065 A196671 A248448 * A245874 A293096 A279888

Adjacent sequences: A248446 A248447 A248448 * A248450 A248451 A248452

Keyword

nonn

Author

R. H. Hardin, Oct 06 2014

Status

approved