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A307666
Number of partitions of n into consecutive positive triangular numbers.
5
1, 0, 1, 1, 0, 1, 0, 0, 1, 2, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2
OFFSET
1,10
COMMENTS
Equivalently, number of ways n can be expressed as the difference between two tetrahedral numbers. - Charlie Neder, Apr 24 2019
Records: a(10)=2, a(2180)=3, a(10053736)=4. - Robert Israel, Aug 20 2019
LINKS
FORMULA
G.f.: Sum_{i>=1} Sum_{j>=i} Product_{k=i..j} x^(k*(k+1)/2).
EXAMPLE
10 = 1 + 3 + 6, so a(10) = 2.
MAPLE
N:= 100:
V:= Vector(N):
for i from 1 while i*(i+1)/2 <= N do
s:= i*(i+1)*(i+2)/6;
for j from i-1 to 0 by -1 do
t:= j*(j+1)*(j+2)/6;
if s-t > N then break fi;
V[s-t]:= V[s-t]+1
od;
od:
convert(V, list); # Robert Israel, Aug 20 2019
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 20 2019
STATUS
approved