A305355 -id:A305355 - cp's OEIS frontend

A305441 Indices k such that A305355(k) = 0.

2, 3, 4, 7, 8, 9, 10, 11, 14, 15, 16, 19, 20, 21, 24, 25, 26, 29, 30, 31, 32, 33, 37, 38, 42, 43, 44, 45, 46, 49, 50, 52, 54, 55, 57, 59, 60, 61, 65, 66, 67, 69, 70, 72, 74, 75, 77, 80, 81, 84, 89, 93, 94, 95, 96, 97, 100, 101, 102, 107, 112, 114, 116, 121, 124, 128

Offset: 1

Seiichi Manyama, Jun 01 2018

nonn

Conjecture: for k > 10316 there are no more terms in this sequence.

			    2 is in the sequence because A305355(    2) = 0.
10316 is in the sequence because A305355(10316) = 0.

Seiichi Manyama, Table of n, a(n) for n = 1..227

Cf. A276517, A305355, A305440.

A292518 Expansion of Product_{k>=1} (1 - x^(k*(k+1)/2)).

Original entry on oeis.org

1, -1, 0, -1, 1, 0, -1, 1, 0, 1, -2, 1, 0, 1, -1, -1, 2, -1, 1, -2, 1, 0, 0, 0, 0, 1, -1, 1, -3, 2, -1, 2, -1, 0, 1, -1, 0, -2, 3, -1, 1, -2, 1, 1, -2, 0, 0, 2, 0, -1, 0, 2, -2, -1, -1, 1, 2, -1, 1, -1, 1, -2, 1, -2, 3, 1, -2, 0, -2, 3, -1, -1, 0, 3, -1, 0, -2, 1, 0, -3, 2, 2, 1, -1, -1, 0, 0, -1, 0, 2, -1

Offset: 0

Ilya Gutkovskiy, Sep 18 2017

sign

Convolution inverse of A007294.
The difference between the number of partitions of n into an even number of distinct triangular numbers and the number of partitions of n into an odd number of distinct triangular numbers.
Euler transform of {-1 if n is a triangular number else 0, n > 0} = -A010054. - Gus Wiseman, Oct 22 2018

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Index entries for related partition-counting sequences

Product_{k>=1} (1 - x^(k*((m-2)*k-(m-4))/2)): this sequence (m=3), A276516 (m=4), A305355 (m=5).

Cf. A007294, A010054, A024940, A280366, A320767, A320784.

nmax = 90; CoefficientList[Series[Product[1 - x^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]

G.f.: Product_{k>=1} (1 - x^(k*(k+1)/2)).

cp's OEIS Frontend

A305441 Indices k such that A305355(k) = 0.

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