OFFSET
0,5
LINKS
Robert Israel, Table of n, a(n) for n = 0..2500
Eric Weisstein's World of Mathematics, Square Number
EXAMPLE
[1 1 1]
[1 4] [1 1 1]
a(23) = 2 because we have [9 9] and [4 4 9].
MAPLE
g:= proc(n, k, m)
# number of partitions of n into k parts which are squares > m^2
option remember; local r;
if k = 0 then if n = 0 then return 1 else return 0 fi fi;
if n < k*(m+1)^2 then return 0 fi;
add(procname(n-r*(m+1)^2, k-r, m+1), r =max(0, ceil((k*(m+2)^2-n)/(2*m+3))) .. k)
end proc:
f:= proc(n) local k; add(g(n, k^2, 0), k=1..floor(sqrt(n))) end proc:
f(0):= 1:
map(f, [$0..100]); # Robert Israel, Oct 26 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 05 2020
STATUS
approved