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

1,2

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).

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)

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 *)

Prog

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

Crossrefs

Cf. A047348, A047355.

Sequence in context: A141489 A060253 A066276 * A270711 A096118 A050029

Adjacent sequences: A047337 A047338 A047339 * A047341 A047342 A047343

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Feb 17 2014

Status

approved