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Search: id:A049235
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| A049235 |
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Sum of balls on the lawn for the s=3 tennis ball problem. |
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7
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| 0, 6, 75, 708, 5991, 47868, 369315, 2783448, 20631126, 151026498, 1094965524, 7878119760, 56330252412, 400703095284, 2838060684483, 20027058300144, 140874026880204, 988194254587242, 6915098239841331, 48285969880645908, 336521149274459979
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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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).
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FORMULA
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a(n) is asymptotic to c*sqrt(n)*(27/4)^n with c=2.4... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 26 2003
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MAPLE
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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;
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CROSSREFS
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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: A066171 A057783 A069852 this_sequence A129031 A139088 A126462
Adjacent sequences: A049232 A049233 A049234 this_sequence A049236 A049237 A049238
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KEYWORD
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nonn
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AUTHOR
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njas, Jan 19 2003
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