A275632 Andrews's 4-shadow function THETA.BAR_3(q).

1, 2, 4, 6, 10, 8, 16, 12, 20, 18, 24, 16, 38, 20, 32, 32, 42, 24, 52, 28, 56, 44, 48, 32, 80, 42, 56, 54, 76, 40, 96, 44, 84, 64, 72, 64, 122, 52, 80, 76, 120, 56, 128, 60, 112, 104, 96, 64, 166, 78, 124, 96, 132, 72, 160, 96

Offset: 0

Author

N. J. A. Sloane, Aug 09 2016

Keywords

• nonn

Links

• R. J. Mathar, Table of n, a(n) for n = 0..999
• George E. Andrews, 4-Shadows in q-Series and the Kimberling Index, Preprint, May 15, 2016

Crossrefs

Cf. A098151, A275633.

Programs

Maple

F:=(a,q,n)->mul(1-a*q^i,i=0..n-1); # This is (a;q)_n
M:=15;
# A098151:
THETA3:=(add((-1)^n*q^(3*n^2),n=-M..M)) /(add((-1)^n*q^(n^2),n=-M..M));
s1:=series(THETA3,q,80); seriestolist(%);
# A275632:
THETABAR3:=1+2*add( (F(q,q,n-1)*q^(n^2)) / (F(q^n,q,n)*(1-q^n)), n=1..M);
s2:=series(THETABAR3,q,80); seriestolist(%);
# A275633:
series((s1-s2)/8,q,80); seriestolist(%);

Formula

See Section 1 of Andrews (2016) or the Maple code below.