

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
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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 BhargavaAdiga 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*(1a*q^j)/(1a*q^(n+j)); od;
t1; end;
D1:=add( (1)^m*q^(m*(m+1))/(B(q, q^2, m+1)*(1q^(2*m+1))), m=0..M):
series(D1, q, M); d1seq:=seriestolist(%);


CROSSREFS

Cf. A008443, A290733A290740.
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



