A079519 Related to tennis ball problem.

12, 284, 5436, 96768, 1664184, 28069444, 467722524, 7730252080, 127023181352, 2078332922360, 33894711502744, 551368536346176, 8950922822411504, 145068948446193428, 2347940754318431196, 37957946888159573968, 613052225104703442120, 9893099103451554441736

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 * A377549 A275007 A262733

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