A047269 Numbers that are congruent to {0, 1, 2, 5} mod 6.

0, 1, 2, 5, 6, 7, 8, 11, 12, 13, 14, 17, 18, 19, 20, 23, 24, 25, 26, 29, 30, 31, 32, 35, 36, 37, 38, 41, 42, 43, 44, 47, 48, 49, 50, 53, 54, 55, 56, 59, 60, 61, 62, 65, 66, 67, 68, 71, 72, 73, 74, 77, 78, 79, 80, 83, 84, 85, 86, 89, 90, 91, 92, 95, 96, 97

Offset

1,3

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

From Colin Barker, May 14 2012: (Start)

a(n) = (-7+(-1)^n+(1+i)*(-i)^n+(1-i)*i^n+6*n)/4 where i=sqrt(-1).

G.f.: x^2*(1+x+3*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)). (End)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Vincenzo Librandi, May 15 2012

a(2n) = A007310(n), a(2n-1) = A047238(n). - Wesley Ivan Hurt, May 22 2016

Sum_{n>=2} (-1)^n/a(n) = log(3)/4 + 2*log(2)/3 - sqrt(3)*Pi/36. - Amiram Eldar, Dec 16 2021

Maple

A047269:=n->(-7+(-1)^n+(1+I)*(-I)^n+(1-I)*I^n+6*n)/4: seq(A047269(n), n=1..100); # Wesley Ivan Hurt, May 22 2016

Mathematica

Select[Range[0, 4000], MemberQ[{0, 1, 2, 5}, Mod[#, 6]]&] (* Vincenzo Librandi, May 15 2012 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 2, 5, 6}, 80] (* Harvey P. Dale, Jun 21 2022 *)

Prog

(Magma) I:=[0, 1, 2, 5, 6]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, May 15 2012
(PARI) x='x+O('x^100); concat(0, Vec(x^2*(1+x+3*x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)))) \\ Altug Alkan, Dec 24 2015

Crossrefs

Cf. A007310, A047238.

Sequence in context: A050007 A047579 A028726 * A039027 A129816 A137708

Adjacent sequences: A047266 A047267 A047268 * A047270 A047271 A047272

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved