A047313 Numbers that are congruent to {1, 4, 5, 6} mod 7.

1, 4, 5, 6, 8, 11, 12, 13, 15, 18, 19, 20, 22, 25, 26, 27, 29, 32, 33, 34, 36, 39, 40, 41, 43, 46, 47, 48, 50, 53, 54, 55, 57, 60, 61, 62, 64, 67, 68, 69, 71, 74, 75, 76, 78, 81, 82, 83, 85, 88, 89, 90, 92, 95, 96, 97, 99, 102, 103, 104, 106, 109, 110, 111

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Crossrefs

Cf. A047288, A047383.

Programs

Magma

[n : n in [0..150] | n mod 7 in [1, 4, 5, 6]]; // Wesley Ivan Hurt, May 23 2016

Maple

A047313:= n-> iquo(n-1, 4, 'r')*7 +[1, 4, 5, 6][r+1]: seq(A047313(n), n=1..80);  # Alois P. Heinz, Dec 04 2011

Mathematica

Select[Range[100],MemberQ[{1,4,5,6},Mod[#,7]]&]  (* Harvey P. Dale, Apr 17 2011 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 4, 5, 6, 8}, 80] (* Jean-François Alcover, Feb 18 2016 *)

Formula

G.f.: x*(1+3*x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Dec 03 2011

From Wesley Ivan Hurt, May 23 2016: (Start)

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

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

a(2n) = A047288(n), a(2n-1) = A047383(n). (End)

E.g.f.: (4 - sin(x) - 3*cos(x) + (7*x - 2)*sinh(x) + (7*x - 1)*cosh(x))/4. - Ilya Gutkovskiy, May 24 2016