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A290735 a(n) = weighted sum over all the self- conjugate partitions of 4n + 1 into odd parts, with respect to a certain weight. 6
1, 2, 2, 3, 4, 3, 5, 6, 4, 6, 7, 6, 7, 8, 6, 7, 11, 7, 8, 10, 6, 11, 12, 7, 10, 12, 8, 11, 13, 8, 11, 16, 10, 9, 15, 8, 13, 18, 9, 14, 14, 10, 15, 16, 10, 13, 20, 11, 13, 20, 8, 17, 22, 8, 14, 17, 15, 18, 20, 12, 14, 23, 12, 14, 20, 12, 21, 25, 9, 16, 22, 14, 21, 22, 12, 15, 26, 16, 14, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See Andrews (2016) for the definition of the particular weight used here.

Andrews (2016), Theorem 2, shows that A008443(n) = A290735(n) + A290737(n) + A290739(n).

Andrews conjectures that a(n) > 0 for all n. The conjecture is known to be true for n <= 1000.

Andrews also conjectures that a(n) > |A290737(n) + A290739(n)| for n >= 2 (see A290740).

LINKS

Table of n, a(n) for n=0..79.

George E. Andrews, The Bhargava-Adiga Summation and Partitions, 2016. See Lemma 3.2.

FORMULA

See Maple code for g.f.

MAPLE

M:=101;

B:=proc(a, q, n) local j, t1; global M; t1:=1;

for j from 0 to M do t1:=t1*(1-a*q^j)/(1-a*q^(n+j)); od;

t1; end;

D1:=add( (-1)^m*q^(m*(m+1))/(B(q, q^2, m+1)*(1-q^(2*m+1))), m=0..M):

series(D1, q, M); d1seq:=seriestolist(%);

CROSSREFS

Cf. A008443, A290733-A290740.

Sequence in context: A091524 A026350 A205002 * A165634 A128282 A146985

Adjacent sequences:  A290732 A290733 A290734 * A290736 A290737 A290738

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 10 2017

STATUS

approved

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Last modified February 24 07:19 EST 2020. Contains 332199 sequences. (Running on oeis4.)