A200867 Number of 0..4 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.

65, 195, 567, 1673, 4917, 14455, 42479, 124851, 366959, 1078565, 3170093, 9317449, 27385589, 80491001, 236577045, 695341043, 2043728099, 6006871845, 17655239697, 51891816107, 152519060911, 448280011791, 1317572818499, 3872575368989

Offset

1,1

Comments

Column 4 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-2) +a(n-3) +4*a(n-4) +a(n-6) +a(n-7).

Empirical g.f.: x*(65 + 47*x^2 + 102*x^3 + 10*x^4 + 30*x^5 + 25*x^6) / (1 - 3*x + x^2 - x^3 - 4*x^4 - x^6 - x^7). - Colin Barker, Oct 16 2017

Example

Some solutions for n=3
..0....1....4....1....1....0....4....0....2....0....2....0....3....4....4....4
..0....4....2....2....4....1....4....0....3....0....2....1....4....1....0....4
..2....4....2....2....4....1....4....1....3....1....0....4....4....0....0....1
..2....4....3....1....2....3....2....1....2....3....0....4....3....0....2....1
..3....3....3....1....2....4....1....1....1....4....1....2....1....3....3....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, 5}]; a[n_] := Sum[a[n, x, y], {x, 5}, {y, 5}]; Array[a, 25] (* Giovanni Resta, Mar 05 2014 *)

Crossrefs

Sequence in context: A261989 A051968 A242318 * A175795 A056777 A048512

Adjacent sequences: A200864 A200865 A200866 * A200868 A200869 A200870

Keyword

nonn

Author

R. H. Hardin, Nov 23 2011

Status

approved