A047246 Numbers that are congruent to {0, 1, 2, 3} mod 6.

0, 1, 2, 3, 6, 7, 8, 9, 12, 13, 14, 15, 18, 19, 20, 21, 24, 25, 26, 27, 30, 31, 32, 33, 36, 37, 38, 39, 42, 43, 44, 45, 48, 49, 50, 51, 54, 55, 56, 57, 60, 61, 62, 63, 66, 67, 68, 69, 72, 73, 74, 75, 78, 79, 80, 81, 84, 85, 86, 87, 90, 91, 92, 93, 96, 97, 98

Offset

1,3

Comments

The sequence is the interleaving of A047238 with A047241. - Guenther Schrack, Feb 12 2019

Links

Reinhard Zumkeller, 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*(1+x+x^2+3*x^3) / ((1+x)*(1-x)^2*(1+x^2)). - R. J. Mathar, Oct 08 2011

a(n) = floor((6/5)*floor(5*(n-1)/4)). - Bruno Berselli, May 03 2016

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

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

a(n) = (6*n - 9 - i^(2*n) - (1-i)*i^(-n) - (1+i)*i^n)/4 where i=sqrt(-1).

a(2*n) = A047241(n), a(2*n-1) = A047238(n). (End)

E.g.f.: (6 + sin(x) - cos(x) + (3*x - 4)*sinh(x) + (3*x - 5)*cosh(x))/2. - Ilya Gutkovskiy, May 21 2016

From Guenther Schrack, Feb 12 2019: (Start)

a(n) = (6*n - 9 - (-1)^n - 2*(-1)^(n*(n+1)/2))/4.

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

Sum_{n>=2} (-1)^n/a(n) = Pi/(6*sqrt(3)) + 2*log(2)/3. - Amiram Eldar, Dec 16 2021

Maple

A047246:=n->(6*n-9-I^(2*n)-(1-I)*I^(-n)-(1+I)*I^n)/4: seq(A047246(n), n=1..100); # Wesley Ivan Hurt, May 21 2016

Mathematica

Table[(6n-9-I^(2n)-(1-I)*I^(-n)-(1+I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 21 2016 *)

Prog

(Haskell)
a047246 n = a047246_list !! (n-1)
a047246_list = [0..3] ++ map (+ 6) a047246_list
-- Reinhard Zumkeller, Jan 15 2013
(Magma) [Floor((6/5)*Floor(5*(n-1)/4)) : n in [1..100]]; // Wesley Ivan Hurt, May 21 2016
(PARI) my(x='x+O('x^70)); concat([0], Vec(x^2*(1+x+x^2+3*x^3)/((1-x)*(1-x^4)))) \\ G. C. Greubel, Feb 16 2019
(Sage) a=(x^2*(1+x+x^2+3*x^3)/((1-x)*(1-x^4))).series(x, 72).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Feb 16 2019
(GAP) Filtered([0..100], n->n mod 6 = 0 or n mod 6 = 1 or n mod 6 = 2 or n mod 6 = 3); # Muniru A Asiru, Feb 20 2019

Crossrefs

Cf. A045331 (primes congruent to {1,2,3} mod 6), A047238, A047241.

Complement: A047257.

Sequence in context: A047287 A039047 A336205 * A039029 A037460 A285134

Adjacent sequences: A047243 A047244 A047245 * A047247 A047248 A047249

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, May 21 2016

Status

approved