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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Programs
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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 *)
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
Comments