A214270 Number of compositions of n where the difference between largest and smallest parts equals 1 and adjacent parts are unequal.

0, 0, 2, 1, 3, 2, 4, 2, 4, 4, 4, 3, 5, 4, 6, 2, 6, 6, 4, 4, 6, 6, 6, 3, 7, 4, 8, 6, 4, 6, 6, 6, 8, 4, 8, 4, 6, 8, 8, 5, 5, 8, 6, 4, 12, 6, 6, 4, 8, 8, 6, 8, 8, 6, 8, 4, 8, 8, 8, 9, 5, 6, 12, 2, 8, 8, 10, 8, 6, 8, 6, 8, 8, 6, 10, 6, 12, 8, 4, 6, 10, 8, 8, 7, 11

Offset: 1

Author

Alois P. Heinz, Jul 09 2012

Keywords

• nonn

Examples

			a(3) = 2: [2,1], [1,2].
a(4) = 1: [1,2,1].
a(5) = 3: [3,2], [2,3], [2,1,2].
a(14) = 4: [5,4,5], [4,3,4,3], [3,4,3,4], [2,1,2,1,2,1,2,1,2].
a(19) = 4: [9,10], [6,7,6], [10,9], [1,2,1,2,1,2,1,2,1,2,1,2,1].
a(25) = 7: [13,12], [12,13], [8,9,8], [4,3,4,3,4,3,4], [3,2,3,2,3,2,3,2,3,2], [2,3,2,3,2,3,2,3,2,3], [1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Column k=1 of A214269.

Programs

Maple

a:= proc(n) local m, r, s, t;
       r, s, t:= 0, 1, 2;
       while s+t<=n do m:= irem(n, s+t);
         r:= r+ `if`(m=0, 2, `if`(m in {s, t}, 1, 0));
         s, t:= s+1, t+1
       od; r
    end:
seq(a(n), n=1..100);

Mathematica

a[n_] := Module[{m, r, s, t}, {r, s, t} = {0, 1, 2}; While[s+t <= n, m = Mod[n, s+t]; r = r+If[m==0, 2, If[m==s || m==t, 1, 0]]; {s, t} = {s+1, t+1}]; r];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 13 2022, after Alois P. Heinz *)