A047340 Numbers that are congruent to {0, 2, 3, 4} mod 7.

0, 2, 3, 4, 7, 9, 10, 11, 14, 16, 17, 18, 21, 23, 24, 25, 28, 30, 31, 32, 35, 37, 38, 39, 42, 44, 45, 46, 49, 51, 52, 53, 56, 58, 59, 60, 63, 65, 66, 67, 70, 72, 73, 74, 77, 79, 80, 81, 84, 86, 87, 88, 91, 93, 94, 95, 98, 100, 101, 102, 105, 107, 108, 109, 112

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A047348, A047355.

Programs

Magma

[n : n in [0..150] | n mod 7 in [0,2,3,4]]; // Vincenzo Librandi, Feb 17 2014

Maple

A047340:=n->(14*n-17-I^(2*n)-(3-I)*I^(-n)-(3+I)*I^n)/8: seq(A047340(n), n=1..100); # Wesley Ivan Hurt, May 21 2016

Mathematica

Select[Range[0,100],MemberQ[{0,2,3,4},Mod[#,7]]&] (* or *) LinearRecurrence[ {1,0,0,1,-1},{0,2,3,4,7},100] (* Harvey P. Dale, Feb 16 2014 *)
CoefficientList[Series[x (2 + x + x^2 + 3 x^3)/((1 + x) (1 + x^2) (x - 1)^2), {x, 0, 200}], x] (* Vincenzo Librandi, Feb 17 2014 *)

Formula

G.f.: x^2*(2+x+x^2+3*x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, May 21 2016: (Start)

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

a(n) = (14n-17-i^(2n)-(3-i)*i^(-n)-(3+i)*i^n)/8 where i=sqrt(-1).

a(2n) = A047348(n), a(2n-1) = A047355(n). (End)

Extensions

More terms from Vincenzo Librandi, Feb 17 2014