A325434 - OEIS

A325434

Row sums of A325433.

0, 1, 1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 47, 60, 80, 101, 133, 167, 216, 270, 344, 428, 540, 667, 834, 1026, 1271, 1555, 1914, 2330, 2849, 3453, 4197, 5065, 6125, 7360, 8858, 10605, 12706, 15155, 18086, 21497, 25557, 30279, 35870, 42366, 50026, 58909, 69346

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OFFSET

1,4

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{k=1..n} ((-1)^(k-1)*Sum_{j=0..k-1} (-1)^j*(p(n - j*(3*j + 1)/2) - p(n - j*(3*j + 5)/2 - 1))), where p(n) = A000041(n) is the number of partitions of n.

Conjecture: Lim_{n->infinity} a(n)/A000041(n) = 1/3.

MATHEMATICA

T[n_, k_]:=(-1)^(k-1)*Sum[(-1)^j*(PartitionsP[n-j*(3*j+1)/2]-PartitionsP[n-j*(3*j+5)/2-1]), {j, 0, k-1}]; (* A325433 *)

Table[Sum[T[n, k], {k, 1, n}], {n, 1, 50}]

PROG

(PARI)

T(n, k) = (-1)^(k-1)*sum(j=0, k-1, (-1)^j*(numbpart(n-j*(3*j+1)/2)-numbpart(n-j*(3*j+5)/2-1))); \\ A325433

a(n) = sum(k=1, n, T(n, k));

CROSSREFS

Cf. A000041, A002865, A325433.

Sequence in context: A104504 A027337 A364892 * A326631 A260894 A193146

Adjacent sequences: A325431 A325432 A325433 * A325435 A325436 A325437

KEYWORD

nonn

AUTHOR

Stefano Spezia, Apr 27 2019

STATUS

approved