A241965 Number of length 2+3 0..n arrays with no consecutive four elements summing to more than 2*n.

19, 124, 486, 1421, 3437, 7280, 13980, 24897, 41767, 66748, 102466, 152061, 219233, 308288, 424184, 572577, 759867, 993244, 1280734, 1631245, 2054613, 2561648, 3164180, 3875105, 4708431, 5679324, 6804154, 8100541, 9587401, 11284992

Offset

1,1

Links

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

Formula

Empirical: a(n) = (23/60)*n^5 + (9/4)*n^4 + (21/4)*n^3 + (25/4)*n^2 + (58/15)*n + 1.

Conjectures from Colin Barker, Oct 31 2018: (Start)

G.f.: x*(19 + 10*x + 27*x^2 - 15*x^3 + 6*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Row 2 of A241964.

Sequence in context: A070302 A125329 A126487 * A182193 A109669 A164905

Adjacent sequences: A241962 A241963 A241964 * A241966 A241967 A241968

Keyword

nonn

Author

R. H. Hardin, May 03 2014

Status

approved