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

1,2

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

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 *)

Prog

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

Crossrefs

Cf. A030123.

Cf. A005009, A030308.

Sequence in context: A190769 A083051 A198269 * A310728 A247157 A087070

Adjacent sequences: A047342 A047343 A047344 * A047346 A047347 A047348

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved