OFFSET
0,3
LINKS
Alois P. Heinz,Table of n, a(n) for n = 0..3607
FORMULA
a(n) ~ c * d^n, where d=1.893587506319686491635881459546948770530553555112342985931092896452453511... and c=0.6398882559654423774981963082429746674258714212085034829366885993226... -Vaclav Kotesovec,May 01 2014
EXAMPLE
There are a(5) = 15 such compositions of 5:
01: [ 1 1 1 1 1 ]
02: [ 1 1 1 2 ]
03: [ 1 1 2 1 ]
04: [ 1 1 3 ]
05: [ 1 2 1 1 ]
06: [ 1 2 2 ]
07: [ 1 3 1 ]
08: [ 2 1 1 1 ]
09: [ 2 1 2 ]
10: [ 2 2 1 ]
11: [ 2 3 ]
12: [ 3 1 1 ]
13: [ 3 2 ]
14: [ 4 1 ]
15: [ 5 ]
(the single forbidden composition is [ 1 4 ]).
MAPLE
b:= proc(n, i) option remember;
`if`(n=0, 1, add(b(n-j, max(1, j-2)), j=i..n))
end:
a:= n-> b(n, 1):
seq(a(n), n=0..40); #Alois P. Heinz,May 02 2013
MATHEMATICA
b[n_, i_]:= b[n, i] = If[n==0, 1, Sum[b[n-j, Max[1, j-2]], {j, i, n}]];
a[n_]:= b[n, 1];
a /@ Range[0, 40] (*Jean-François Alcover,Dec 19 2020, afterAlois P. Heinz*)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt,Apr 21 2013
STATUS
approved