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

1,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A047288, A047383.

Sequence in context: A209722 A035067 A027698 * A030343 A030590 A047430

Adjacent sequences: A047310 A047311 A047312 * A047314 A047315 A047316

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved