A047362 Numbers that are congruent to {2, 3, 4, 5} mod 7.

2, 3, 4, 5, 9, 10, 11, 12, 16, 17, 18, 19, 23, 24, 25, 26, 30, 31, 32, 33, 37, 38, 39, 40, 44, 45, 46, 47, 51, 52, 53, 54, 58, 59, 60, 61, 65, 66, 67, 68, 72, 73, 74, 75, 79, 80, 81, 82, 86, 87, 88, 89, 93, 94, 95, 96, 100, 101, 102, 103, 107, 108, 109, 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. A047348, A047389.

Programs

Magma

[n : n in [0..150] | n mod 7 in [2, 3, 4, 5]]; // Wesley Ivan Hurt, Jun 03 2016

Maple

A047362:=n->(14*n-7-3*(I^(2*n)+(1-I)*I^(-n)+(1+I)*I^n))/8: seq(A047362(n), n=1..100); # Wesley Ivan Hurt, Jun 03 2016

Mathematica

Select[Range[100], MemberQ[{2,3,4,5}, Mod[#,7]]&] (* or *) LinearRecurrence[{1,0,0,1,-1}, {2,3,4,5,9}, 60] (* Harvey P. Dale, Oct 03 2015 *)

Formula

G.f.: x*(2*x^2+3*x+2)*(x^2-x+1) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, Jun 03 2016: (Start)

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

a(n) = (14*n-7-3*(i^(2*n)+(1-i)*i^(-n)+(1+i)*i^n))/8 where i=sqrt(-1).

a(2k) = A047389(k), a(2k-1) = A047348(k). (End)