A047365 Numbers that are congruent to {0, 3, 4, 5} mod 7.

0, 3, 4, 5, 7, 10, 11, 12, 14, 17, 18, 19, 21, 24, 25, 26, 28, 31, 32, 33, 35, 38, 39, 40, 42, 45, 46, 47, 49, 52, 53, 54, 56, 59, 60, 61, 63, 66, 67, 68, 70, 73, 74, 75, 77, 80, 81, 82, 84, 87, 88, 89, 91, 94, 95, 96, 98, 101, 102, 103, 105, 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. A047345, A047389.

Programs

Magma

[n : n in [0..150] | n mod 7 in [0, 3, 4, 5]]; // Wesley Ivan Hurt, Jun 04 2016

Maple

A047365:=n->(14*n-11+I^(2*n)-(3+I)*I^(-n)-(3-I)*I^n)/8: seq(A047365(n), n=1..100); # Wesley Ivan Hurt, Jun 04 2016

Mathematica

Select[Range[0,100], MemberQ[{0,3,4,5}, Mod[#,7]]&] (* or *) LinearRecurrence[{1,0,0,1,-1}, {0,3,4,5,7}, 60] (* Harvey P. Dale, May 26 2012 *)

Formula

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

a(1)=0, a(2)=3, a(3)=4, a(4)=5, a(5)=7, a(n)=a(n-1)+a(n-4)-a(n-5) for n>5. - Harvey P. Dale, May 26 2012

From Wesley Ivan Hurt, Jun 04 2016: (Start)

a(n) = (14*n-11+i^(2*n)-(3+i)*i^(-n)-(3-i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047389(k), a(2k-1) = A047345(k). (End)