OFFSET
0,4
COMMENTS
This sequence is in reply to an extension request made in A100450.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000 (terms n = 0..200 from Robert Price)
Cristina Ballantine, George Beck, Mircea Merca, and Bruce Sagan, Elementary symmetric partitions, arXiv:2409.11268 [math.CO], 2024. See p. 20.
FORMULA
a(n) = (A213207(n)+1)/2.
MAPLE
h:= proc() true end:
b:= proc(n) local c, i, j, p;
c:=0;
for i to iquo(n, 3) do
for j from i to iquo(n-i, 2) do p:= i*j*(n-i-j);
if h(p) then h(p):= false; c:=c+1 fi
od
od; c
end:
a:= proc(n) a(n):= `if`(n=0, 1, a(n-1) +b(n)) end:
seq(a(n), n=0..60); # Alois P. Heinz, Mar 02 2013
MATHEMATICA
f[n_] := Length[ Union[ Flatten[ Table[ If[ i+j+k <= n, i*j*k, 0], {i, 0, n}, {j, 0, n}, {k, 0, n}], 2]]]; Table[ f[n], {n, 0, 200}]
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Robert Price, Mar 02 2013
STATUS
approved