OFFSET
1,3
COMMENTS
Previous (incorrect) name was: Maximum number of lines in a game of sprouts with n initial dots. The correct formula for that name is A016789(n-1). - Andrey Zabolotskiy, Feb 19 2018
REFERENCES
E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 564.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
D. Purvis, World Game of Sprouts Association
Index entries for linear recurrences with constant coefficients, signature (2, -1).
FORMULA
a(1)=0, a(2)=1, a(3)=8, a(4)=11, a(n)=2*a(n-1)-a(n-2). - Harvey P. Dale, Dec 12 2011
G.f.: x^2*(1+6*x-4*x^2)/(1-x)^2. - Colin Barker, Apr 12 2012
MATHEMATICA
Join[{0, 1}, 3*Range[2, 60]+2] (* or *) Join[{0, 1}, LinearRecurrence[{2, -1}, {8, 11}, 60]] (* Harvey P. Dale, Dec 12 2011 *)
PROG
(GAP) Concatenation([0, 1], List([3..60], n->3*n-1)); # Muniru A Asiru, Feb 20 2018
(PARI) a(n) = if(n<3, n-1, 3*n-1); \\ Altug Alkan, Feb 20 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Eric Shafto (eshafto(AT)mac.com), May 18 2001
EXTENSIONS
New name from Andrey Zabolotskiy, Feb 19 2018
STATUS
approved