A072836 Exponents occurring in expansion of F_10(q^2).

0, 9, 16, 20, 21, 24, 25, 29, 36, 40, 41, 44, 45, 49, 56, 60, 61, 64, 65, 69, 76, 80, 81, 84, 85, 89, 96, 100, 101, 104, 105, 109, 116, 120, 121, 124, 125, 129, 136, 140, 141, 144, 145, 149, 156, 160, 161, 164, 165, 169, 176, 180, 181, 184, 185, 189, 196, 200, 201, 204, 205, 209, 216

Offset: 0

Author

N. J. A. Sloane, Jul 25 2002

Keywords

• nonn
• easy

Comments

Nonnegative numbers congruent to {0, 1, 4, 5, 9, 16} (mod 20), except for {1, 4, 5}. Also, norms of vectors in the A*9 lattice. - _Andrey Zabolotskiy, Nov 10 2021

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• S. Ahlgren, The sixth, eighth, ninth and tenth powers of Ramanujan's theta function, Proc. Amer. Math. Soc. 128 (2000), 1333-1338
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Crossrefs

Cf. A023921.

Programs

Mathematica

f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; F[10,q_]:= f[q^5, q^5]^10/f[q, q] - 8*q^2*f[q^5, q^5]^5* QPochhammer[q^10]^5/QPochhammer[q^2] - (27*q^4*f[q^5, q^5]^5 - 125*q^9*f[q^5, q^5]*f[q^10, q^30]^4 + 5*q^5*f[q^5, q^5]*f[q^2, q^6]^4)* QPochhammer[q^20]^5/QPochhammer[q^4] - 17*q^5*f[q, q]*f[q^5, q^15]^8 + 2*q*f[q, q]*f[q^5, q^5]^4*f[q^2, q^6]^4 - 20*q^8*f[q, q]*QPochhammer[q^20]^10/QPochhammer[q^4]^2 + 5*q^4*f[q, q]*QPochhammer[q^10]^10/QPochhammer[q^2]^2; cfs = CoefficientList[Series[F[10, q], {q, 0, 500}], q]; Take[Pick[Range[Length[cfs]] - 1, Sign[Abs[cfs]], 1], 50] (* G. C. Greubel, Apr 16 2018 *)

Formula

G.f.: -x*(5*x^6-x^5-3*x^4-x^3-4*x^2-7*x-9) / (x^7-x^6-x+1). - Colin Barker, Jul 31 2013

a(n) = 20*floor((n-1)/6)+9,16,20,21,24,25 for n == 1,2,3,4,5,0 (mod 6) respectively, for n>0. - Jerzy R Borysowicz, Oct 23 2022

Extensions

Terms a(27) onward added by G. C. Greubel, Apr 16 2018