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), 188-192. 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) 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).
FORMULA
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
MATHEMATICA
Join[{0, 1, 3}, NestList[#+2&, 4, 60]] (* Harvey P. Dale, Apr 01 2012 *)
PROG
(PARI) a(n)=if(n>3, 2*n-4, [0, 1, 3][n]) \\ Charles R Greathouse IV, Feb 10 2017
CROSSREFS
KEYWORD
easy,nonn,nice
AUTHOR
Torsten Sillke (torsten.sillke(at)lhsystems.com), Jan 17 2001
STATUS
approved