A241966 Number of length 3+3 0..n arrays with no consecutive four elements summing to more than 2*n.

33, 311, 1597, 5778, 16660, 40978, 89622, 179079, 333091, 584529, 977483, 1569568, 2434446, 3664564, 5374108, 7702173, 10816149, 14915323, 20234697, 27049022, 35677048, 46485990, 59896210, 76386115, 96497271, 120839733, 150097591

Offset

1,1

Links

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

Formula

Empirical: a(n) = (3/10)*n^6 + (127/60)*n^5 + (149/24)*n^4 + (59/6)*n^3 + (1079/120)*n^2 + (91/20)*n + 1.

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

G.f.: x*(33 + 80*x + 113*x^2 - 25*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Row 3 of A241964.

Sequence in context: A024400 A297492 A256109 * A210077 A210070 A258638

Adjacent sequences: A241963 A241964 A241965 * A241967 A241968 A241969

Keyword

nonn

Author

R. H. Hardin, May 03 2014

Status

approved