OFFSET
1,2
COMMENTS
Nonnegative k such that k or 5*k + 1 is divisible by 7. - Bruno Berselli, Feb 13 2018
Maximum number of 2's possible in an infinite Minesweeper grid with n mines. The pattern of mines (x) that generates these 2's looks like "...xx.xx.xx...". - Dmitry Kamenetsky, Apr 14 2018
LINKS
David Lovler, Table of n, a(n) for n = 1..1000
Wikipedia, Minesweeper.
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = ceiling(7*(n-1)/2).
a(n) = 7*n - a(n-1) - 10 for n>1, a(1)=0. - Vincenzo Librandi, Aug 05 2010
From R. J. Mathar, Oct 08 2011: (Start)
a(n) = 7*n/2 - 13/4 + (-1)^n/4.
G.f.: x^2*(4 + 3*x) / ((1 + x)*(x - 1)^2). (End)
a(n+1) = Sum_{k>=0} A030308(n,k)*b(k), with b(0) = 4, b(k) = A005009(k-1) = 7*2^(k-1), and k>0. - Philippe Deléham, Oct 17 2011.
a(n) = 4*(n - 1) - floor((n - 1)/2). - Wesley Ivan Hurt, Jun 14 2013
a(n) = 2*(n - 1) + floor((3*n - 2 - (n mod 2))/2). - Wesley Ivan Hurt, Mar 31 2014
E.g.f.: 3 + ((14*x - 13)*exp(x) + exp(-x))/4. - David Lovler, Aug 31 2022
MAPLE
MATHEMATICA
Table[Ceiling[7 (n - 1)/2], {n, 100}] (* Wesley Ivan Hurt, Mar 31 2014 *)
PROG
(PARI) forstep(n=0, 200, [4, 3], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved