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A079521 Triangular array related to tennis ball problem, read by rows. 3
0, 1, 2, 3, 5, 4, 10, 16, 13, 6, 31, 47, 45, 25, 8, 105, 158, 145, 96, 41, 10, 343, 501, 500, 340, 175, 61, 12, 1198, 1752, 1673, 1226, 676, 288, 85, 14, 4056, 5808, 5898, 4326, 2569, 1205, 441, 113, 16, 14506, 20868, 20312, 15608, 9526, 4836, 1987, 640, 145, 18, 50350, 71218, 73000, 55696, 35448, 18800, 8418, 3090, 891, 181, 20 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Rows n=0..100 of triangle, flattened

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

FORMULA

Let c, d, and g be given by: 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*c(t))^r*(t*c(t)^3 + 2*r*c(t)) then the rows are calculated by the expansion of g(t,k) for n>=0, 0 <= k <= n. - G. C. Greubel, Jan 17 2019

EXAMPLE

0.

1,   2.

3,   5,   4.

10,  16,  13,  6.

31,  47,  45,  25, 8.

105, 158, 145, 96, 41, 10. ...

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*c[t])^r*(t*c[t]^3 +2*r*c[t]); Table[SeriesCoefficient[Series[g[t, k], {t, 0, n}], n], {n, 0, 10}, {k, 0, n}] (* G. C. Greubel, Jan 17 2019 *)

CROSSREFS

Leading diagonal gives A079522.

Cf. A079513, A079520, A079521.

Sequence in context: A066417 A254669 A227913 * A325549 A112060 A084933

Adjacent sequences:  A079518 A079519 A079520 * A079522 A079523 A079524

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Jan 22 2003

EXTENSIONS

Terms a(28) onward added by G. C. Greubel, Jan 17 2019

STATUS

approved

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Last modified November 20 05:07 EST 2019. Contains 329323 sequences. (Running on oeis4.)