A047307 Numbers that are congruent to {3, 4, 5, 6} mod 7.

3, 4, 5, 6, 10, 11, 12, 13, 17, 18, 19, 20, 24, 25, 26, 27, 31, 32, 33, 34, 38, 39, 40, 41, 45, 46, 47, 48, 52, 53, 54, 55, 59, 60, 61, 62, 66, 67, 68, 69, 73, 74, 75, 76, 80, 81, 82, 83, 87, 88, 89, 90, 94, 95, 96, 97, 101, 102, 103, 104, 108, 109, 110, 111

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. A047288, A047389.

Programs

Magma

[n : n in [0..150] | n mod 7 in [3, 4, 5, 6]]; // Wesley Ivan Hurt, Jun 02 2016

Maple

A047307:=n->(14*n+1-3*I^(2*n)-(3-3*I)*I^(-n)-(3+3*I)*I^n)/8: seq(A047307(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016

Mathematica

Table[(14n+1-3*I^(2*n)-(3-3*I)*I^(-n)-(3+3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 02 2016 *)
LinearRecurrence[{1,0,0,1,-1},{3,4,5,6,10},70] (* Harvey P. Dale, Dec 28 2024 *)

Formula

G.f.: x*(3+x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 25 2011

From Wesley Ivan Hurt, Jun 02 2016: (Start)

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

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

a(2k) = A047288(k), a(2k-1) = A047389(k). (End)