A200870 Number of 0..7 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.

232, 932, 3704, 14932, 60112, 241718, 971416, 3904290, 15693816, 63085186, 253583656, 1019321774, 4097329180, 16469898636, 66203547550, 266116375576, 1069699742484, 4299838717346, 17283927781406, 69475666835578

Offset

1,1

Comments

Column 7 of A200871.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -2*a(n-2) +4*a(n-3) +15*a(n-4) +6*a(n-5) +12*a(n-6) +16*a(n-7) +7*a(n-8) +5*a(n-9) +4*a(n-10) +a(n-11).

Empirical g.f.: 2*x*(116 + 2*x + 220*x^2 + 526*x^3 + 292*x^4 + 473*x^5 + 552*x^6 + 257*x^7 + 180*x^8 + 132*x^9 + 32*x^10) / (1 - 4*x + 2*x^2 - 4*x^3 - 15*x^4 - 6*x^5 - 12*x^6 - 16*x^7 - 7*x^8 - 5*x^9 - 4*x^10 - x^11). - Colin Barker, Oct 16 2017

Example

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

Mathematica

a[0, x_, y_] := 1; a[n_, x_, y_] := a[n, x, y] = Sum[If[z <=x<= y || y <=x<= z, a[n-1, z, x], 0], {z, 8}]; a[n_] := Sum[a[n, x, y], {x, 8}, {y, 8}]; Array[a, 25] (* Giovanni Resta, Mar 05 2014 *)

Crossrefs

Sequence in context: A245006 A252273 A153466 * A357573 A234690 A234683

Adjacent sequences: A200867 A200868 A200869 * A200871 A200872 A200873

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved