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A058992
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Gossip Problem: there are n people and each of them knows some item of gossip not known to the others. They communicate by telephone and whenever one person calls another, they tell each other all that they know at that time. How many calls are required before each gossip knows everything?
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5
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0, 1, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124
(list;
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OFFSET
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1,3
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COMMENTS
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The sequence (for n>=1) refers to the famous "nine dots puzzle" as well. It represents the minimum number of straight lines that you need to fit the centers of n^2 dots (without lifting the pencil from the paper). - Marco Ripà, Apr 01 2013
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REFERENCES
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R. Tijdeman, On a telephone problem. Nieuw Arch. Wisk. (3) 19 (1971), 188-192. Math. Rev. 49 #7151
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
B. Baker and R. Shostak, Gossips and Telephones, Discrete Mathematics 2 (1972) 191-193. Math. Rev. 46 # 68.
R. T. Bumby, A problem with telephones, SIAM J. Alg. Disc. Meth. 2 (1981) 13-18. Math. Rev. 82f:05083.
A. Hajnal, E. C. Milner and E. Szemeredi, A cure for the telephone disease Canad. Math. Bull. 15 (1972), 447-450. Math. Rev. 47 #3184.
D. J. Kleitman and J. B. Shearer, Further Gossip Problems, Discrete Mathematics 30 (1980), 151-156. Math. Rev. 81d:05068.
M. Ripà, nxnx...xn Dots Puzzle
T. Sillke, References
T. Sillke, Proofs
Wikipedia, nine dots puzzle
Index entries for linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
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a(n) = 2n - 4 for n >= 4.
G.f.: x^2*(1+x-x^2+x^3)/(1-x)^2. - Colin Barker, Jun 07 2012
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MATHEMATICA
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Join[{0, 1, 3}, NestList[#+2&, 4, 60]] (* Harvey P. Dale, Apr 01 2012 *)
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PROG
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(PARI) a(n)=if(n>3, 2*n-4, [0, 1, 3][n]) \\ Charles R Greathouse IV, Feb 10 2017
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CROSSREFS
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Cf. A007456.
Sequence in context: A184736 A173472 A334905 * A051755 A092535 A215476
Adjacent sequences: A058989 A058990 A058991 * A058993 A058994 A058995
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Torsten Sillke (torsten.sillke(at)lhsystems.com), Jan 17 2001
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STATUS
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approved
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