A047345 Numbers that are congruent to {0, 4} mod 7.

0, 4, 7, 11, 14, 18, 21, 25, 28, 32, 35, 39, 42, 46, 49, 53, 56, 60, 63, 67, 70, 74, 77, 81, 84, 88, 91, 95, 98, 102, 105, 109, 112, 116, 119, 123, 126, 130, 133, 137, 140, 144, 147, 151, 154, 158, 161, 165, 168, 172, 175, 179, 182, 186, 189, 193

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A030123.

Cf. A005009, A030308.

Programs

Maple

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

Mathematica

Table[Ceiling[7 (n - 1)/2], {n, 100}] (* Wesley Ivan Hurt, Mar 31 2014 *)

PARI

forstep(n=0,200,[4,3],print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011

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