OFFSET
0,3
LINKS
Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..45
EXAMPLE
The a(5) = 13 such compositions are:
01: [ 1 1 2 1 ]
02: [ 1 1 3 ]
03: [ 1 2 1 1 ]
04: [ 1 2 2 ]
05: [ 1 3 1 ]
06: [ 1 4 ]
07: [ 2 1 2 ]
08: [ 2 2 1 ]
09: [ 2 3 ]
10: [ 3 1 1 ]
11: [ 3 2 ]
12: [ 4 1 ]
13: [ 5 ]
Note that the first and third composition contain the progression 1,1,1, but not in equidistant positions.
MAPLE
b:= proc(n, l) local j;
for j from 2 to iquo(nops(l)+1, 2) do
if l[1]-l[j]=l[j]-l[2*j-1] then return 0 fi od;
`if`(n=0, 1, add(b(n-i, [i, l[]]), i=1..n))
end:
a:= n-> b(n, []):
seq(a(n), n=0..20);
MATHEMATICA
b[n_, l_] := b[n, l] = Module[{j}, For[j = 2, j <= Quotient[Length[l] + 1, 2], j++, If[l[[1]] - l[[j]] == l[[j]] - l[[2*j - 1]], Return[0]]]; If[n == 0, 1, Sum[b[n - i, Prepend[l, i]], {i, 1, n}]]];
a[n_] := b[n, {}];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 21 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Mar 01 2014
STATUS
approved