The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A079518 Coefficients related to tennis ball problem. 6
1, 28, 462, 6832, 97957, 1394180, 19862674, 284156608, 4086496362, 59089988216, 858975619676, 12549322976672, 184195104642157, 2715174884250004, 40181870424263146, 596810833742837536, 8893877150513222014, 132947157383427373320, 1992954280253792526660 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344. (Table A.3)
FORMULA
With c(t) = (1 - sqrt(1-4*t))/(2*t), d(t) = (1 -(1+2*t)*sqrt(1-4*t) -(1 - 2*t)*sqrt(1+4*t) + sqrt(1-16*t^2))/(4*t^2), and g(t, r) = d(t)*t^(r + 1)*c(t)^(r + 3) then the g.f. is given by the even terms in the expansion of g(t,3) = 1*t^4 + 28*t^6 + 462*t^8 + 6832*t^10 + ... - G. C. Greubel, Jan 16 2019
MATHEMATICA
c[t_]:= (1-Sqrt[1-4*t])/(2*t); d[t_]:= (1-(1+2*t)*Sqrt[1-4*t] -(1- 2*t)*Sqrt[1+4*t] + Sqrt[1-16*t^2])/(4*t^2); g[t_, r_]:= d[t]*t^(r+1)*c[t]^(r+3); Drop[CoefficientList[Series[g[t, 3], {t, 0, 60}], t][[1;; ;; 2]], 2] (* G. C. Greubel, Jan 16 2019 *)
CROSSREFS
Sequence in context: A000771 A327508 A215767 * A320820 A160060 A115226
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 22 2003
EXTENSIONS
Terms a(5) onward added by G. C. Greubel, Jan 16 2019
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 May 25 17:30 EDT 2024. Contains 372804 sequences. (Running on oeis4.)