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

1,1

Links

Table of n, a(n) for n=1..64.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

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)

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 *)

Prog

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

Crossrefs

Cf. A047288, A047389.

Sequence in context: A353568 A364146 A059877 * A179774 A138918 A071186

Adjacent sequences: A047304 A047305 A047306 * A047308 A047309 A047310

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved