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A378961
Number of sets of nonzero triangular numbers whose largest element is the n-th triangular number and whose sum is a triangular number.
2
1, 1, 2, 1, 3, 5, 5, 11, 19, 33, 55, 92, 192, 327, 579, 1142, 2052, 3776, 6936, 12964, 24308, 44432, 84763, 159299, 299093, 567295, 1075570, 2045580, 3883453, 7411014, 14164089, 27044407, 51759660, 99259961, 190371661, 365537357, 702901278, 1352868238, 2606296357
OFFSET
1,3
LINKS
EXAMPLE
a(5) = 3 subsets of triangular numbers whose largest element is A000217(5)=15 and whose sum is in A000217: {15}, {6, 15} and {3, 10, 15}.
MAPLE
istri:= proc(n) issqr(1+8*n) end proc:
tri:= n -> n*(n+1)/2:
F:= proc(n, s) option remember; local v;
if s = 0 then return 1 fi;
if s > n*(n+1)*(n+2)/6 then return 0 fi;
v:= tri(n);
if s >= v then procname(n-1, s-v) + procname(n-1, s)
else procname(n-1, s)
fi;
end proc:
f:= proc(n) local i, t, m;
t:= 0;
m:= n*(n+1)*(n+2)/6;
for i from 1 while tri(i) <= m do
t:= t + F(n, tri(i)) - F(n-1, tri(i))
od;
t
end proc:
map(f, [$1..50]); # Robert Israel, Jan 13 2025
CROSSREFS
Cf. A000217, A339612, A339613, A377123 (partial sums).
Sequence in context: A296064 A167595 A328600 * A179382 A161169 A239738
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 12 2024
STATUS
approved