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A307666
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Number of partitions of n into consecutive positive triangular numbers.
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5
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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
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OFFSET
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1,10
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COMMENTS
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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
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LINKS
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FORMULA
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G.f.: Sum_{i>=1} Sum_{j>=i} Product_{k=i..j} x^(k*(k+1)/2).
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EXAMPLE
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10 = 1 + 3 + 6, so a(10) = 2.
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MAPLE
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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:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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