OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
Jonathan Bloom, Nathan McNew, Counting pattern-avoiding integer partitions, arXiv:1908.03953 [math.CO], 2019.
FORMULA
EXAMPLE
MAPLE
g := add(x^i/(1-x^i), i = 1 .. 80)+add(add(x^(i+j)/((1-x^i)*(1-x^j)), j = i+1..80), i=1..80): gser := series(g, x=0, 60): seq(coeff(gser, x, n), n=1..50);
# second Maple program:
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(i<1, 0,
`if`(t=1, `if`(irem(n, i)=0, 1, 0)+b(n, i-1, t),
add(b(n-i*j, i-1, t-`if`(j=0, 0, 1)), j=0..n/i))))
end:
a:= n-> b(n$2, 2):
seq(a(n), n=1..100); # Alois P. Heinz, Jan 01 2016
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, If[i < 1, 0, If[t == 1, If[Mod[n, i] == 0, 1, 0] + b[n, i - 1, t], Sum[b[n - i*j, i - 1, t - If[j == 0, 0, 1]], {j, 0, n/i}]]]]; a[n_] := b[n, n, 2]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Dec 22 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Emeric Deutsch, Dec 25 2015
STATUS
approved