A047392 Numbers that are congruent to {0, 1, 3, 5} mod 7.

0, 1, 3, 5, 7, 8, 10, 12, 14, 15, 17, 19, 21, 22, 24, 26, 28, 29, 31, 33, 35, 36, 38, 40, 42, 43, 45, 47, 49, 50, 52, 54, 56, 57, 59, 61, 63, 64, 66, 68, 70, 71, 73, 75, 77, 78, 80, 82, 84, 85, 87, 89, 91, 92, 94, 96, 98, 99, 101, 103, 105, 106, 108, 110

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A047355, A047383.

Cf. A047371: n + floor(3*n/4-1/2) - 1; A047379: n + floor(3*n/4-1/4) - 1.

Programs

Magma

[n: n in [0..100] | n mod 7 in [0, 1, 3, 5]]; // Wesley Ivan Hurt, May 21 2016

Maple

A047392:=n->(14*n-17-I^(2*n)+(1+I)*I^(-n)+(1-I)*I^n)/8: seq(A047392(n), n=1..100); # Wesley Ivan Hurt, May 21 2016

Mathematica

Table[(14n-17-I^(2n)+(1+I)*I^(-n)+(1-I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 21 2016 *)
Table[n + Floor[3 n/4 - 3/4] - 1, {n, 1, 70}] (* Bruno Berselli, Jun 15 2016 *)

Formula

G.f.: x^2*(1+2*x+2*x^2+2*x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, May 21 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (14*n - 17 - i^(2*n) + (1 + i)*i^(-n) + (1 - i)*i^n)/8.

a(2k) = A047383(k), a(2k-1) = A047355(k). (End)

a(n) = n + floor(3*n/4-3/4) - 1. - Bruno Berselli, Jun 15 2016

Extensions

More terms from Wesley Ivan Hurt, May 21 2016