OFFSET
0,4
COMMENTS
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
N. J. A. Sloane and B. K. Teo, Theta series and magic numbers for close-packed spherical clusters, J. Chem. Phys. 83 (1985) 6520-6534. See page 6530 equation 66.
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of x^3 * ( f(x^3, x^15) * (f(x^16, x^32) * f(x^15, x^39) + x^6 * f(x^8, x^40) * f(x^3, x^51)) + f(x^6, x^12) * (f(x^16, x^32) * f(x^12, x^42) + f(x^8, x^40) * f(x^24, x^30)) ) in powers of x where f(, ) is Ramanujan's general theta function. - Michael Somos, Feb 11 2018
G.f.: Sum{i, j, k in Z} x^(9*(i*i + i*j + j*j) + 24*k*k) * (x^(6 - 12*(i+j) - 8*k) + x^(3 - 3*(i+j) + 16*k)). - Michael Somos, Feb 11 2018
EXAMPLE
G.f. = 3*x^3 + x^6 + 3*x^9 + x^11 + 2*x^12 + 4*x^15 + 2*x^17 + 2*x^18 + 2*x^19 + ...
MATHEMATICA
f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; a[n_] := SeriesCoefficient[x^3*(f[x^3, x^15]*(f[x^16, x^32]* f[x^15, x^39] + x^6*f[x^8, x^40]*f[x^3, x^51]) + f[x^6, x^12]*(f[x^16, x^32]*f[x^12, x^42] + f[x^8, x^40]*f[x^24, x^30])), {x, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Apr 02 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved