A242146 Number of length 2+5 0..n arrays with no consecutive six elements summing to more than 3*n.

74, 1113, 7862, 36224, 126894, 367358, 924300, 2088459, 4333978, 8394287, 15356562, 26776802, 44817566, 72410412, 113445080, 172987461, 257528394, 375265333, 536418926, 753586548, 1042134830, 1420633226, 1911330660

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1021/2520)*n^7 + (28/9)*n^6 + (3679/360)*n^5 + (1349/72)*n^4 + (1873/90)*n^3 + (1019/72)*n^2 + (779/140)*n + 1.

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

G.f.: x*(74 + 521*x + 1030*x^2 + 348*x^3 + 90*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Row 2 of A242144.

Sequence in context: A204353 A300487 A222861 * A007033 A277941 A017790

Adjacent sequences: A242143 A242144 A242145 * A242147 A242148 A242149

Keyword

nonn

Author

R. H. Hardin, May 05 2014

Status

approved