A047362 Numbers that are congruent to {2, 3, 4, 5} mod 7.

2, 3, 4, 5, 9, 10, 11, 12, 16, 17, 18, 19, 23, 24, 25, 26, 30, 31, 32, 33, 37, 38, 39, 40, 44, 45, 46, 47, 51, 52, 53, 54, 58, 59, 60, 61, 65, 66, 67, 68, 72, 73, 74, 75, 79, 80, 81, 82, 86, 87, 88, 89, 93, 94, 95, 96, 100, 101, 102, 103, 107, 108, 109, 110

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*(2*x^2+3*x+2)*(x^2-x+1) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 04 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-7-3*(i^(2*n)+(1-i)*i^(-n)+(1+i)*i^n))/8 where i=sqrt(-1).

a(2k) = A047389(k), a(2k-1) = A047348(k). (End)

Maple

A047362:=n->(14*n-7-3*(I^(2*n)+(1-I)*I^(-n)+(1+I)*I^n))/8: seq(A047362(n), n=1..100); # Wesley Ivan Hurt, Jun 03 2016

Mathematica

Select[Range[100], MemberQ[{2, 3, 4, 5}, Mod[#, 7]]&] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {2, 3, 4, 5, 9}, 60] (* Harvey P. Dale, Oct 03 2015 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [2, 3, 4, 5]]; // Wesley Ivan Hurt, Jun 03 2016

Crossrefs

Cf. A047348, A047389.

Sequence in context: A158573 A194398 A047603 * A032969 A095906 A333050

Adjacent sequences: A047359 A047360 A047361 * A047363 A047364 A047365

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved