OFFSET
0,14
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Kevin Beanland and Hung Viet Chu, On Schreier-type Sets, Partitions, and Compositions, arXiv:2311.01926 [math.CO], 2023.
FORMULA
a(n) = A026826(n+5). - R. J. Mathar, Jul 31 2008
G.f.: Product_{j>=6} (1+x^j). - R. J. Mathar, Jul 31 2008
G.f.: Sum_{k>=0} x^(k*(k + 11)/2) / Product_{j=1..k} (1 - x^j). - Ilya Gutkovskiy, Nov 24 2020
MAPLE
b:= proc(n, i) option remember;
`if`(n=0, 1, `if`((i-5)*(i+6)/2<n, 0,
add(b(n-i*j, i-1), j=0..min(1, n/i))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..100); # Alois P. Heinz, Feb 07 2014
MATHEMATICA
d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 && Min[#] >= 6 &]; Table[d[n], {n, 16}] (* strict partitions, parts >= 6 *)
Table[Length[d[n]], {n, 40}] (* A025151 for n >= 1 *)
(* Clark Kimberling, Mar 07 2014 *)
b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i - 5)(i + 6)/2 < n, 0, Sum[b[n - i j, i - 1], {j, 0, Min[1, n/i]}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Aug 29 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved