OFFSET
0,3
COMMENTS
Although a(n) != 0 for 2 <= n <= 62, it seems that most terms are zero. There are only 1351 nonzero terms among a(0) through a(10000).
a(n) is odd if and only if n != 4 and n/2 is in A000009.
Conjecture: a(n) = 0, 1, 2, 4, 6 for all n > 29696.
LINKS
Jianing Song, Table of n, a(n) for n = 0..30000
FORMULA
EXAMPLE
MATHEMATICA
Table[Length@Select[Tuples[k=1; While[Max[p=PartitionsQ/@Range[0, k++]]<n]; Most@p, {2}], Total@#==n&], {n, 0, 100}] (* Giorgos Kalogeropoulos, Sep 21 2021 *)
PROG
(PARI) leng(n) = for(l=0, oo, if(A000009(l)>n-1, return(l))) \\ See A000009 for its program; A000009(0), A000009(1), ..., A000009(l-1) <= n-1
v(n) = my(l=leng(n), v=[]); for(i=0, l-1, v=concat(v, vector(l, j, A000009(i)+A000009(j-1)))); v=vecsort(v); v
list(n) = my(v=v(n), w=vector(n), size=#v); for(i=1, size, if(v[i]<=n, w[v[i]]++, break())); w=concat([0], w); w
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Sep 20 2021
STATUS
approved