A047312 Numbers that are congruent to {0, 4, 5, 6} mod 7.

0, 4, 5, 6, 7, 11, 12, 13, 14, 18, 19, 20, 21, 25, 26, 27, 28, 32, 33, 34, 35, 39, 40, 41, 42, 46, 47, 48, 49, 53, 54, 55, 56, 60, 61, 62, 63, 67, 68, 69, 70, 74, 75, 76, 77, 81, 82, 83, 84, 88, 89, 90, 91, 95, 96, 97, 98, 102, 103, 104, 105, 109, 110, 111

Offset

1,2

Links

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

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

Formula

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

From Wesley Ivan Hurt, Jun 03 2016: (Start)

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

a(n) = (14*n-5+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) = A047382(k). (End)

Maple

A047312:=n->(14*n-5+3*I^(2*n)-(3+3*I)*I^(-n)-(3-3*I)*I^n)/8: seq(A047312(n), n=1..100); # Wesley Ivan Hurt, Jun 03 2016

Mathematica

Table[(14n-5+3*I^(2n)-(3+3*I)*I^(-n)-(3-3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, Jun 03 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [0, 4, 5, 6]]; // Wesley Ivan Hurt, Jun 03 2016

Crossrefs

Cf. A047288, A047382.

Sequence in context: A364803 A022561 A213524 * A191164 A363089 A004714

Adjacent sequences: A047309 A047310 A047311 * A047313 A047314 A047315

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved