A047345 - OEIS

%I #60 Sep 01 2022 09:52:10

%S 0,4,7,11,14,18,21,25,28,32,35,39,42,46,49,53,56,60,63,67,70,74,77,81,

%T 84,88,91,95,98,102,105,109,112,116,119,123,126,130,133,137,140,144,

%U 147,151,154,158,161,165,168,172,175,179,182,186,189,193

%N Numbers that are congruent to {0, 4} mod 7.

%C Nonnegative k such that k or 5*k + 1 is divisible by 7. - _Bruno Berselli_, Feb 13 2018

%C 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

%H David Lovler, <a href="/A047345/b047345.txt">Table of n, a(n) for n = 1..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Minesweeper_(video_game)">Minesweeper</a>.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(n) = ceiling(7*(n-1)/2).

%F a(n) = 7*n - a(n-1) - 10 for n>1, a(1)=0. - _Vincenzo Librandi_, Aug 05 2010

%F From _R. J. Mathar_, Oct 08 2011: (Start)

%F a(n) = 7*n/2 - 13/4 + (-1)^n/4.

%F G.f.: x^2*(4 + 3*x) / ((1 + x)*(x - 1)^2). (End)

%F 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.

%F a(n) = 4*(n - 1) - floor((n - 1)/2). - _Wesley Ivan Hurt_, Jun 14 2013

%F a(n) = 2*(n - 1) + floor((3*n - 2 - (n mod 2))/2). - _Wesley Ivan Hurt_, Mar 31 2014

%F E.g.f.: 3 + ((14*x - 13)*exp(x) + exp(-x))/4. - _David Lovler_, Aug 31 2022

%p A047345:=n->ceil(7*(n-1)/2); seq(A047345(n), n=1..100); # _Wesley Ivan Hurt_, Mar 31 2014

%t Table[Ceiling[7 (n - 1)/2], {n, 100}] (* _Wesley Ivan Hurt_, Mar 31 2014 *)

%o (PARI) forstep(n=0,200,[4,3],print1(n", ")) \\ _Charles R Greathouse IV_, Oct 17 2011

%Y Cf. A030123.

%Y Cf. A005009, A030308.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_