login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A047246 Numbers that are congruent to {0, 1, 2, 3} mod 6. 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 (list; graph; refs; listen; history; text; internal format)
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)

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: A163099 A047287 A039047 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 04:55 EST 2019. Contains 329110 sequences. (Running on oeis4.)