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A072833 Numbers that are congruent to 0, 5, 8, 9 mod 12. 3
0, 5, 8, 9, 12, 17, 20, 21, 24, 29, 32, 33, 36, 41, 44, 45, 48, 53, 56, 57, 60, 65, 68, 69, 72, 77, 80, 81, 84, 89, 92, 93, 96, 101, 104, 105, 108, 113, 116, 117, 120, 125, 128, 129, 132, 137, 140, 141, 144, 149, 152, 153, 156, 161, 164, 165, 168, 173, 176, 177, 180, 185, 188, 189 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The exponents occurring in the expansion of F_6(q^2) (see Ahlgren) or, equivalently, the norms of the vectors in the A*_5 lattice are all in this list and probably include all numbers in this list. - Andrey Zabolotskiy, Aug 14 2020
LINKS
S. Ahlgren, The sixth, eighth, ninth and tenth powers of Ramanujan's theta function, Proc. Amer. Math. Soc. 128 (2000), 1333-1338.
FORMULA
G.f.: x*(3*x^2-2*x+5) / ((x-1)^2*(x^2+1)). - Colin Barker, Jul 31 2013
MATHEMATICA
(* This program is based on the function F_6(q^2), so it is not proved that it generates all terms. *) f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; F[6, q_]:= ( -3*f[q, q]^5 + 5*f[q, q]^3*f[q^3, q^3]^2 + 15*f[q, q]*f[q^3, q^3]^4 + 15*f[q^3, q^3]^6/f[q, q] )/32; cfs = CoefficientList[Series[F[6, q], {q, 0, 500}], q]; Take[Pick[Range[Length[cfs]] - 1, Sign[Abs[cfs]], 1], 50] (* G. C. Greubel, Apr 16 2018 *)
Flatten[#+{0, 5, 8, 9}&/@(12*Range[0, 20])] (* Harvey P. Dale, Apr 10 2022 *)
CROSSREFS
Sequence in context: A314573 A066467 A180244 * A229469 A314574 A314575
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 25 2002
EXTENSIONS
Terms a(33) onward added by G. C. Greubel, Apr 16 2018
Edited by Andrey Zabolotskiy, Aug 14 2020
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)