A249885 Number of length 2+6 0..n arrays with no seven consecutive terms having the maximum of any three terms equal to the minimum of the remaining four terms.

35, 1365, 18390, 136010, 684585, 2644815, 8435180, 23274900, 57355695, 129095945, 269791170, 530015070, 988165685, 1761591555, 3020773080, 5007074600, 8054623035, 12616909245, 19298748590, 28894277490, 42431703105, 61225563575

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^8 + (16/7)*n^7 + (16/3)*n^6 + 8*n^5 + (59/6)*n^4 + 7*n^3 + (4/3)*n^2 + (3/14)*n.

Conjectures from Colin Barker, Nov 10 2018: (Start)

G.f.: 5*x*(7 + 210*x + 1473*x^2 + 3340*x^3 + 2457*x^4 + 546*x^5 + 31*x^6) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

Example

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

Crossrefs

Row 2 of A249883.

Sequence in context: A158733 A029560 A195617 * A135923 A180883 A130005

Adjacent sequences: A249882 A249883 A249884 * A249886 A249887 A249888

Keyword

nonn

Author

R. H. Hardin, Nov 07 2014

Status

approved