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A049235 Sum of balls on the lawn for the s=3 tennis ball problem. 7
0, 6, 75, 708, 5991, 47868, 369315, 2783448, 20631126, 151026498, 1094965524, 7878119760, 56330252412, 400703095284, 2838060684483, 20027058300144, 140874026880204, 988194254587242, 6915098239841331, 48285969880645908, 336521149274459979 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344 (S_n for s=3).

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) is asymptotic to c*sqrt(n)*(27/4)^n with c=2.4... - Benoit Cloitre, Jan 26 2003

G.f.: F(G^(-1)(x)) where F = 3*(2-3*t)*t*((t-1)*(3*t-1))^(-3) and G = t*(t-1)^2   - Mark van Hoeij, Oct 30 2011.

MAPLE

T := (n, s)->binomial(s*n, n)/((s-1)*n+1); Y := (n, s)->add(binomial(s*k, k)*binomial(s*(n-k), n-k), k=0..n); A := (n, s)->Y(n+1, s)/2-(1/2)*((2*s-3)*n+2*s-2)*T(n+1, s); S := (n, s)->(1/2)*(s*n^2+(3*s-1)*n+2*s)*T(n+1, s)-Y(n+1, s)/2;

F := 3*(2-3*t)*t*((t-1)*(3*t-1))^(-3);  G := t*(t-1)^2;   Ginv := RootOf(G-x, t);

ogf := series(eval(F, t=Ginv), x=0, 20);

CROSSREFS

The four sequences T_n, Y_n, A_n, S_n for s=2 are A000108, A000302, A000346, A031970, for s=3, A001764, A006256, A075045, this sequence, for s=4, A002293, A078995, A078999, A078516.

Cf. A079486.

Sequence in context: A266574 A258270 A281797 * A129031 A234529 A139088

Adjacent sequences:  A049232 A049233 A049234 * A049236 A049237 A049238

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 19 2003

STATUS

approved

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Last modified December 12 00:07 EST 2018. Contains 318052 sequences. (Running on oeis4.)