A200837 Number of 0..7 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

400, 2444, 15128, 93472, 577660, 3570086, 22063924, 136360286, 842739040, 5208328180, 32188710564, 198933910242, 1229459024390, 7598350081290, 46959616234372, 290221631449614, 1793638920327662, 11085116434803236

Offset

1,1

Comments

Column 7 of A200838.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) -12*a(n-2) +6*a(n-3) -10*a(n-4) +12*a(n-5) -11*a(n-6) +11*a(n-7) -6*a(n-8) +3*a(n-9) -a(n-10).

Empirical g.f.: 2*x*(200 - 378*x + 188*x^2 - 312*x^3 + 378*x^4 - 329*x^5 + 338*x^6 - 183*x^7 + 92*x^8 - 32*x^9) / (1 - 8*x + 12*x^2 - 6*x^3 + 10*x^4 - 12*x^5 + 11*x^6 - 11*x^7 + 6*x^8 - 3*x^9 + x^10). - Colin Barker, Oct 16 2017

Example

Some solutions for n=3
..7....3....6....6....2....3....0....3....7....0....2....1....1....0....3....0
..2....3....5....0....3....5....4....2....1....5....0....0....7....0....2....3
..7....6....6....4....2....5....2....7....4....4....4....5....3....4....2....3
..4....1....6....0....5....5....5....1....2....7....0....0....4....2....6....0
..7....5....5....5....2....3....0....1....4....6....0....4....4....4....5....0

Crossrefs

Sequence in context: A061042 A223481 A037991 * A250847 A043400 A038483

Adjacent sequences: A200834 A200835 A200836 * A200838 A200839 A200840

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved