This site is supported by donations to The OEIS Foundation. Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A045836 Half of Theta series of b.c.c. lattice with respect to long edge. 1
 1, 2, 0, 0, 4, 4, 0, 0, 5, 4, 0, 0, 4, 8, 0, 0, 8, 6, 0, 0, 8, 4, 0, 0, 5, 12, 0, 0, 12, 8, 0, 0, 8, 8, 0, 0, 4, 12, 0, 0, 16, 8, 0, 0, 12, 8, 0, 0, 9, 14, 0, 0, 12, 16, 0, 0, 8, 4, 0, 0, 12, 16, 0, 0, 16, 16, 0, 0, 16, 8, 0, 0, 8, 20, 0, 0, 16, 8, 0, 0, 17 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). The body-centered cubic (b.c.c. also known as D3*) lattice is the set of all triples [a, b, c] where the entries are all integers or all one half an odd integer. A long edge is centered at a triple with two integer entries and the remaining entry is one half an odd integer. - Michael Somos, May 31 2012 LINKS Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Contribution from Michael Somos, May 31 2012: (Start) Expansion of x * phi(x) * psi(x^4)^2 = x * psi(-x^2)^4 / phi(-x) in powers of x where phi(), psi() are Ramanujan theta functions. Expansion of eta(q^2)^5 * eta(q^8)^4 / (eta(q)^2 * eta(q^4)^4) in powers of q. Euler transform of period 8 sequence [ 2, -3, 2, 1, 2, -3, 2, -3, ...]. a(4*n) = a(4*n + 3) = 0. a(n) = 2 * A004025(n). a(4*n + 1) = A045834(n). a(4*n + 2) = 2 * A045828(n). (End) EXAMPLE q + 2*q^2 + 4*q^5 + 4*q^6 + 5*q^9 + 4*q^10 + 4*q^13 + 8*q^14 + 8*q^17 + ... MATHEMATICA a[n_] := Module[{A = x*O[x]^n}, SeriesCoefficient[QPochhammer[x^2+A]^5 * (QPochhammer[x^8+A]^4 / (QPochhammer[x+A]^2*QPochhammer[x^4+A]^4)), {x, 0, n}]]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Nov 05 2015, adapted from PARI *) PROG (PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^8 + A)^4 / (eta(x + A)^2 * eta(x^4 + A)^4), n))} /* Michael Somos, May 31 2012 */ CROSSREFS Cf. A004025, A045828, A045834. Sequence in context: A004531 A072071 A329264 * A182056 A072070 A137830 Adjacent sequences:  A045833 A045834 A045835 * A045837 A045838 A045839 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 22:27 EST 2019. Contains 329880 sequences. (Running on oeis4.)