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A307666 Number of partitions of n into consecutive positive triangular numbers. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Equivalently, number of ways n can be expressed as the difference between two tetrahedral numbers. - Charlie Neder, Apr 24 2019

LINKS

Table of n, a(n) for n=1..100.

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.

CROSSREFS

Cf. A000217, A001227, A007294, A024940, A034706, A296338, A307614.

Sequence in context: A256852 A128616 A270417 * A319995 A266344 A174875

Adjacent sequences:  A307663 A307664 A307665 * A307667 A307668 A307669

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 20 2019

STATUS

approved

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Last modified July 21 18:13 EDT 2019. Contains 325199 sequences. (Running on oeis4.)