A047380 Numbers that are congruent to {1, 2, 4, 5} mod 7.

1, 2, 4, 5, 8, 9, 11, 12, 15, 16, 18, 19, 22, 23, 25, 26, 29, 30, 32, 33, 36, 37, 39, 40, 43, 44, 46, 47, 50, 51, 53, 54, 57, 58, 60, 61, 64, 65, 67, 68, 71, 72, 74, 75, 78, 79, 81, 82, 85, 86, 88, 89, 92, 93, 95, 96, 99, 100, 102, 103, 106, 107, 109, 110

Offset

1,2

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*(1+x+2*x^2+x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, May 20 2016: (Start)

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

a(n) = (14*n - 11 - 3*i^(2*n) - (1+i)*i^(-n-1) - (1-i)*i^(n+1))/8 where i=sqrt(-1).

a(2n) = A047385(n), a(2n-1) = A047346(n). (End)

Maple

A047380:=n->(14*n-11-3*I^(2*n)-(1+I)*I^(-n-1)-(1-I)*I^(n+1))/8: seq(A047380(n), n=1..100); # Wesley Ivan Hurt, May 20 2016

Mathematica

Table[(14n-11-3I^(2n)-(1+I)I^(-n-1)-(1-I)I^(n+1))/8, {n, 80}] (* Wesley Ivan Hurt, May 20 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 4, 5, 8}, 100] (* Harvey P. Dale, Jun 05 2016 *)

Prog

(PARI) a(n)=(n-1)\4*7+[5, 1, 2, 4][n%4+1] \\ Charles R Greathouse IV, Jun 11 2015

Crossrefs

Cf. A002265, A047346, A047385.

Sequence in context: A286031 A027883 A201818 * A288214 A376090 A117121

Adjacent sequences: A047377 A047378 A047379 * A047381 A047382 A047383

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved