

A058992


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?


5



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
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OFFSET

1,3


COMMENTS

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


REFERENCES

R. Tijdeman, On a telephone problem. Nieuw Arch. Wisk. (3) 19 (1971), 188192. Math. Rev. 49 #7151


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
B. Baker and R. Shostak, Gossips and Telephones, Discrete Mathematics 2 (1972) 191193. Math. Rev. 46 # 68.
R. T. Bumby, A problem with telephones, SIAM J. Alg. Disc. Meth. 2 (1981) 1318. Math. Rev. 82f:05083.
A. Hajnal, E. C. Milner and E. Szemeredi, A cure for the telephone disease Canad. Math. Bull. 15 (1972), 447450. Math. Rev. 47 #3184.
D. J. Kleitman and J. B. Shearer, Further Gossip Problems, Discrete Mathematics 30 (1980), 151156. 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).


FORMULA

a(n) = 2n  4 for n >= 4.
G.f.: x^2*(1+xx^2+x^3)/(1x)^2.  Colin Barker, Jun 07 2012


MATHEMATICA

Join[{0, 1, 3}, NestList[#+2&, 4, 60]] (* Harvey P. Dale, Apr 01 2012 *)


PROG

(PARI) a(n)=if(n>3, 2*n4, [0, 1, 3][n]) \\ Charles R Greathouse IV, Feb 10 2017


CROSSREFS

Cf. A007456.
Sequence in context: A191262 A184736 A173472 * A051755 A092535 A215476
Adjacent sequences: A058989 A058990 A058991 * A058993 A058994 A058995


KEYWORD

easy,nonn,nice


AUTHOR

Torsten Sillke (torsten.sillke(at)lhsystems.com), Jan 17 2001


STATUS

approved



