A047262 Numbers that are congruent to {0, 2, 4, 5} mod 6.

0, 2, 4, 5, 6, 8, 10, 11, 12, 14, 16, 17, 18, 20, 22, 23, 24, 26, 28, 29, 30, 32, 34, 35, 36, 38, 40, 41, 42, 44, 46, 47, 48, 50, 52, 53, 54, 56, 58, 59, 60, 62, 64, 65, 66, 68, 70, 71, 72, 74, 76, 77, 78, 80, 82, 83, 84, 86, 88, 89, 90, 92, 94, 95, 96, 98

Offset

1,2

Comments

The sequence is the interleaving of A047233 with A016789(n-1). - Guenther Schrack, Feb 14 2019

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Index entries for two-way infinite sequences.

Formula

From R. J. Mathar, Oct 08 2011: (Start)

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

a(n) = 3*n/2 - 1 - sin(Pi*n/2)/2. (End)

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

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n > 4.

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

a(2*n) = A016789(n-1) for n>0, a(2*n-1) = A047233(n).

a(2-n) = - A047237(n), a(n-1) = A047273(n) - 1 for n > 1. (End)

From Guenther Schrack, Feb 14 2019: (Start)

a(n) = (6*n - 4 - (1 - (-1)^n)*(-1)^(n*(n-1)/2))/4.

a(n) = a(n-4) + 6, a(1)=0, a(2)=2, a(3)=4, a(4)=5, for n > 4. (End)

Sum_{n>=2} (-1)^n/a(n) = log(3)/4 + log(2)/3 - sqrt(3)*Pi/36. - Amiram Eldar, Dec 17 2021

Maple

A047262:=n->(6*n-4-I^(1-n)+I^(1+n))/4: seq(A047262(n), n=1..100); # Wesley Ivan Hurt, May 21 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 2, 4, 5}, Mod[#, 6]]&] (* or *) LinearRecurrence[{2, -2, 2, -1}, {0, 2, 4, 5}, 70] (* Harvey P. Dale, Dec 09 2015 *)

Prog

(Magma) [n : n in [0..100] | n mod 6 in [0, 2, 4, 5]]; // Wesley Ivan Hurt, May 21 2016
(PARI) my(x='x+O('x^70)); concat([0], Vec(x^2*(2+x^2)/((1+x^2)*(1-x)^2))) \\ G. C. Greubel, Feb 16 2019
(Sage) a=(x^2*(2+x^2)/((1+x^2)*(1-x)^2)).series(x, 72).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Feb 16 2019

Crossrefs

Cf. A016789, A047233, A047237, A047273.

Complement: A047241.

Sequence in context: A285354 A050505 A340932 * A361233 A285143 A274436

Adjacent sequences: A047259 A047260 A047261 * A047263 A047264 A047265

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, May 21 2016

Status

approved