A061570 a(1)=0, a(2)=1, a(n)=3*n-1 for n >= 3.

0, 1, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173, 176, 179

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

Cf. A016789.

Sequence in context: A153039 A190208 A363364 * A096679 A262443 A287552

Adjacent sequences: A061567 A061568 A061569 * A061571 A061572 A061573

Keyword

easy,nonn

Author

Eric Shafto (eshafto(AT)mac.com), May 18 2001

Extensions

New name from Andrey Zabolotskiy, Feb 19 2018

Status

approved