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

1,3

Links

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

Example

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].

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 *)

Crossrefs

Column k=1 of A214269.

Sequence in context: A028914 A204539 A302604 * A289440 A290636 A106466

Adjacent sequences: A214267 A214268 A214269 * A214271 A214272 A214273

Keyword

nonn

Author

Alois P. Heinz, Jul 09 2012

Status

approved