login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A079519 Related to tennis ball problem. 5
12, 284, 5436, 96768, 1664184, 28069444, 467722524, 7730252080, 127023181352, 2078332922360, 33894711502744, 551368536346176, 8950922822411504, 145068948446193428, 2347940754318431196, 37957946888159573968, 613052225104703442120, 9893099103451554441736 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..500

D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344. (Table A.4)

FORMULA

Let f, g, S1 and S3 be given by f(t) = sqrt(1-4*t), g(t) = sqrt(1+4*t), S1(t) = (1+f(t)-2*f(t)^2)*(1- f(t))^5/(t^3*(f(t)^2-f(t))^2*(2+f(t)+g(t))^2), S3(t) = 4*(1-f(t))^2*(1 -g(t))^2*(f(t)^2-(1+2*t)*f(t)-(1-6*t)*g(t)+f(t)*g(t))/(t^3*(2+f(t)+ g(t))^2*(g(t)^2-f(t)-g(t)+ f(t)*g(t))^2). Now let W(t) be given by W(t) = (S1(t) + S1(-t) + S3(t) + S3(-t))/4. The g.f. is the expansion of W(t). - G. C. Greubel, Jan 17 2019

EXAMPLE

G.f. = 12*t^2 + 284*t^4 + 5436*t^6 + 96768*t^8 + ... - G. C. Greubel, Jan 17 2019

MATHEMATICA

f[t_]:= Sqrt[1-4*t]; g[t_]:= Sqrt[1+4*t]; S1[t_]:= (1+f[t]-2*f[t]^2)*(1- f[t])^5/(t^3*(f[t]^2-f[t])^2*(2+f[t]+g[t])^2); S3[t_]:= 4*(1-f[t])^2*(1 -g[t])^2*(f[t]^2-(1+2*t)*f[t]-(1-6*t)*g[t]+f[t]*g[t])/(t^3*(2+f[t]+ g[t])^2*(g[t]^2-f[t]-g[t]+f[t]*g[t])^2); W[t_]:= (S1[t]+S1[-t]+S3[t]+ S3[-t])/4; Drop[CoefficientList[Series[W[t], {t, 0, 50}], t][[1 ;; ;; 2]], 1] (* G. C. Greubel, Jan 17 2019 *)

CROSSREFS

Cf. A079513, A079514, A079515, A079516, A079517, A079518, A079520.

Sequence in context: A183767 A009604 A154669 * A275007 A262733 A296736

Adjacent sequences:  A079516 A079517 A079518 * A079520 A079521 A079522

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 22 2003

EXTENSIONS

Terms a(5) onward added by G. C. Greubel, Jan 17 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 6 01:03 EDT 2021. Contains 343579 sequences. (Running on oeis4.)