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A031970
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Tennis ball problem: Balls 1 and 2 are thrown into a room; you throw one on lawn; then balls 3 and 4 are thrown in and you throw any of the 3 balls onto the lawn; then balls 5 and 6 are thrown in and you throw one of the 4 balls onto the lawn; after n turns, consider all possible collections on lawn and add all the values.
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2
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0, 3, 23, 131, 664, 3166, 14545, 65187, 287060, 1247690, 5368670, 22917198, 97195968, 410030812, 1722027973, 7204620067, 30044212828, 124932768082, 518215690018
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344.
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LINKS
| Colin L. Mallows and Lou Shapiro, Balls on the Lawn, J. Integer Sequences, Vol. 2, 1999, #5.
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FORMULA
| Colin L. Mallows (colinm(AT)research.avayalabs.com) found the formula (2n^2 + 5n + 4)*(2n+1 choose n)/(n+2) - 2^(2n+1).
Computed from rows of "New" Catalan triangle T[n,i] = A028364. S(n) = Sum{i=0..n-1}(4*n-4*i-1)T[n,i]. e.g. for n=3 T[3..] = [5,7,9,14] then S(3) = 131 = 11*5 + 7*7 + 3*9 [From David J Scambler (dscambler(AT)bmm.com), Apr 27 2009]
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CROSSREFS
| Cf. A049235, A078516, A079486, A000108.
Sequence in context: A196424 A091055 A154648 * A196881 A049164 A081413
Adjacent sequences: A031967 A031968 A031969 * A031971 A031972 A031973
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KEYWORD
| nonn
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AUTHOR
| Louis Shapiro (lshapiro(AT)howard.edu)
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