OFFSET
0,3
COMMENTS
Also number of partitions of n in which each part, with the possible exception of the largest, occurs at least 8 times.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz)
FORMULA
G.f.: 1 + Sum_{j>=1} x^j/(1-x^j) * Product_{i=1..j-1} (1+x^(8*i)/(1-x^i)).
log(a(n)) ~ sqrt((2*Pi^2/3 + 4*c)*n), where c = Integral_{0..infinity} log(1 - exp(-x) + exp(-8*x)) dx = -1.1447921975208768146551512630331558734964408879... - Vaclav Kotesovec, Jan 28 2022
EXAMPLE
a(9) = 3: [1,1,1,1,1,1,1,1,1], [3,3,3], [9].
a(10) = 5: [1,1,1,1,1,1,1,1,1,1], [2,2,2,2,2], [5,5], [1,9], [10].
a(11) = 4: [1,1,1,1,1,1,1,1,1,1,1], [1,1,9], [1,10], [11].
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1) +add(b(n-i*j, i-8), j=1..n/i)))
end:
a:= n-> b(n, n):
seq(a(n), n=0..70);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 04 2012
STATUS
approved