login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A045826 a(n) = A005887(n) / 2. 6
3, 4, 12, 0, 15, 12, 12, 0, 24, 12, 24, 0, 15, 16, 36, 0, 24, 24, 12, 0, 48, 12, 36, 0, 27, 24, 36, 0, 24, 36, 36, 0, 48, 12, 48, 0, 24, 28, 48, 0, 51, 36, 24, 0, 72, 24, 24, 0, 24, 36, 84, 0, 48, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
Expansion of q^(-1) * (phi^3(q) - phi^3(-q)) / 4 in powers of q^2 where phi() is a Ramanujan theta function. - Michael Somos, Mar 12 2011
A005875(2*n + 1) = 2 * a(n). - Michael Somos, Mar 12 2011
EXAMPLE
3 + 4*x + 12*x^2 + 15*x^4 + 12*x^5 + 12*x^6 + 24*x^8 + 12*x^9 + ...
3*q + 4*q^3 + 12*q^5 + 15*q^9 + 12*q^11 + 12*q^13 + 24*q^17 + 12*q^19 + ...
MATHEMATICA
A005887[n_]:= SeriesCoefficient[(EllipticTheta[3, 0, q]^3 - EllipticTheta[3, 0, -q]^3)/(2 q), {q, 0, n}]; Table[A005887[n]/2, {n, 0, 50}][[1;; ;; 2]] (* G. C. Greubel, Feb 09 2018 *)
PROG
(PARI) {a(n) = if( n<0, 0, n = 2*n + 1; polcoeff( sum( k=1, sqrtint(n), 2 * x^k^2, 1 + x*O(x^n))^3 / 2, n))} /* Michael Somos, Mar 12 2011 */
CROSSREFS
Sequence in context: A041299 A001112 A042079 * A346471 A084200 A348997
KEYWORD
nonn
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)