A200868 Number of 0..5 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.

106, 356, 1168, 3886, 12890, 42744, 141688, 469726, 1557320, 5163158, 17117854, 56752072, 188154290, 623802050, 2068138180, 6856654898, 22732385492, 75366392740, 249867889178, 828405870894, 2746476505360, 9105600837300

Offset

1,1

Comments

Column 5 of A200871.

Links

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

Formula

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

Empirical g.f.: 2*x*(53 + 19*x + 50*x^2 + 138*x^3 + 67*x^4 + 48*x^5 + 57*x^6 + 18*x^7) / (1 - 3*x - x^3 - 7*x^4 - 3*x^5 - 2*x^6 - 3*x^7 - x^8). - Colin Barker, Oct 16 2017

Example

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

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, 6}]; a[n_] := Sum[a[n, x, y], {x, 6}, {y, 6}]; Array[a, 25] (* Giovanni Resta, Mar 06 2014 *)

Crossrefs

Sequence in context: A090775 A213458 A260937 * A234421 A234414 A090037

Adjacent sequences: A200865 A200866 A200867 * A200869 A200870 A200871

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved