A250420 Number of length 3+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

10, 38, 99, 205, 370, 606, 927, 1345, 1874, 2526, 3315, 4253, 5354, 6630, 8095, 9761, 11642, 13750, 16099, 18701, 21570, 24718, 28159, 31905, 35970, 40366, 45107, 50205, 55674, 61526, 67775, 74433, 81514, 89030, 96995, 105421, 114322, 123710, 133599

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5).

Empirical for n mod 2 = 0: a(n) = (13/6)*n^3 + (13/4)*n^2 + (10/3)*n + 1.

Empirical for n mod 2 = 1: a(n) = (13/6)*n^3 + (13/4)*n^2 + (10/3)*n + (5/4).

Empirical g.f.: x*(10 + 8*x + 5*x^2 + 4*x^3 - x^4) / ((1 - x)^4*(1 + x)). - Colin Barker, Nov 14 2018

Example

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

Crossrefs

Row 3 of A250419.

Sequence in context: A034859 A197060 A257051 * A136840 A027982 A064603

Adjacent sequences: A250417 A250418 A250419 * A250421 A250422 A250423

Keyword

nonn

Author

R. H. Hardin, Nov 22 2014

Status

approved