OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = A277100(n,0).
G.f.: g(x) = Product_{i>=1}(1/(1-x^(i+1)) - x^(i(i+1))).
EXAMPLE
a(4) = 4 because we have [1,1,1,1], [1,3], [2,2], and [4]; the partition [1,1,2] does not qualify.
MAPLE
g := (product(1/(1-x^(i+1))-x^(i*(i+1)), i = 1 .. 100))/(1-x): gser := series(g, x = 0, 53): seq(coeff(gser, x, n), n = 0 .. 50);
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(`if`(i-1=j, 0, b(n-i*j, i-1)), j=0..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..60); # Alois P. Heinz, Oct 10 2016
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[If[i-1 == j, 0, b[n-i*j, i-1]], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Dec 11 2016 after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Oct 10 2016
STATUS
approved