A200836 Number of 0..6 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

273, 1491, 8239, 45465, 250913, 1384813, 7642875, 42181611, 232803603, 1284861277, 7091249941, 39137163521, 216001069269, 1192126810953, 6579441195743, 36312451033865, 200411259993515, 1106085433196691

Offset

1,1

Comments

Column 6 of A200838.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) -9*a(n-2) +6*a(n-3) -9*a(n-4) +7*a(n-5) -7*a(n-6) +5*a(n-7) -2*a(n-8) +a(n-9).

Empirical g.f.: x*(273 - 420*x + 259*x^2 - 427*x^3 + 320*x^4 - 319*x^5 + 236*x^6 - 91*x^7 + 49*x^8) / (1 - 7*x + 9*x^2 - 6*x^3 + 9*x^4 - 7*x^5 + 7*x^6 - 5*x^7 + 2*x^8 - x^9). - Colin Barker, Oct 15 2017

Example

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

Crossrefs

Sequence in context: A157374 A043467 A028530 * A276980 A350303 A214220

Adjacent sequences: A200833 A200834 A200835 * A200837 A200838 A200839

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved