OFFSET
8,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 8..1000
FORMULA
G.f.: Sum_{i>0} x^(2*i+8) / Product_{j=1..8+i} (1-x^j).
EXAMPLE
a(10) = 1: [9,1].
a(11) = 1: [9,1,1].
a(12) = 3: [9,1,1,1], [9,2,1], [10,2].
a(13) = 4: [9,1,1,1,1], [9,2,1,1], [9,3,1], [10,2,1].
a(14) = 8: [9,1,1,1,1,1], [9,2,1,1,1], [9,2,2,1], [9,3,1,1], [9,4,1], [10,2,1,1], [10,2,2], [11,3].
MAPLE
b:= proc(n, i) option remember;
`if`(n=0 or i=1, 1, b(n, i-1)+`if`(i>n, 0, b(n-i, i)))
end:
a:= n-> add(b(n-2*m-8, min(n-2*m-8, m+8)), m=1..(n-8)/2):
seq(a(n), n=8..60);
MATHEMATICA
Table[Count[IntegerPartitions[n], _?(MemberQ[#, Max[#]-8]&)], {n, 8, 55}] (* Harvey P. Dale, May 05 2016 *)
b[n_, i_] := b[n, i] = If[n == 0 || i == 1, 1, b[n, i - 1] + If[i > n, 0, b[n - i, i]]];
a[n_] := Sum[b[n - 2 m - 8, Min[n - 2 m - 8, m + 8]], {m, 1, (n - 8)/2}];
a /@ Range[8, 60] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 20 2012
STATUS
approved