A008588 Nonnegative multiples of 6.

0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324, 330, 336, 342, 348

Offset

0,2

Comments

For n > 3, the number of squares on the infinite 3-column half-strip chessboard at <= n knight moves from any fixed point on the short edge.

Second differences of A000578. - Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004

A008615(a(n)) = n. - Reinhard Zumkeller, Feb 27 2008

A157176(a(n)) = A001018(n). - Reinhard Zumkeller, Feb 24 2009

These numbers can be written as the sum of four cubes (i.e., 6*n = (n+1)^3 + (n-1)^3 + (-n)^3 + (-n)^3). - Arkadiusz Wesolowski, Aug 09 2013

A122841(a(n)) > 0 for n > 0. - Reinhard Zumkeller, Nov 10 2013

Surface area of a cube with side sqrt(n). - Wesley Ivan Hurt, Aug 24 2014

a(n) is representable as a sum of three but not two consecutive nonnegative integers, e.g., 6 = 1 + 2 + 3, 12 = 3 + 4 + 5, 18 = 5 + 6 + 7, etc. (see A138591). - Martin Renner, Mar 14 2016 (Corrected by David A. Corneth, Aug 12 2016)

Numbers with three consecutive divisors: for some k, each of k, k+1, and k+2 divide n. - Charles R Greathouse IV, May 16 2016

Numbers k for which {phi(k),phi(2k),phi(3k)} is an arithmetic progression. - Ivan Neretin, Aug 12 2016

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 318

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

Formula

From Vincenzo Librandi, Dec 24 2010: (Start)

a(n) = 6*n = 2*a(n-1) - a(n-2).

G.f.: 6*x/(1-x)^2. (End)

a(n) = Sum_{k>=0} A030308(n,k)*6*2^k. - Philippe Deléham, Oct 24 2011

a(n) = Sum_{k=2n-1..2n+1} k. - Wesley Ivan Hurt, Nov 22 2015

From Ilya Gutkovskiy, Aug 12 2016: (Start)

E.g.f.: 6*x*exp(x).

Convolution of A010722 and A057427.

Sum_{n>=1} (-1)^(n+1)/a(n) = log(2)/6 = A002162*A020793. (End)

a(n) = 6 * A001477(n). - David A. Corneth, Aug 12 2016

Maple

[ seq(6*n, n=0..45) ];

Mathematica

Range[0, 500, 6] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)

Prog

(Magma) [6*n: n in [0..60] ]; // Vincenzo Librandi, Jul 16 2011
(PARI) a(n)=6*n \\ Charles R Greathouse IV, Feb 08 2012
(Maxima) makelist(6*n, n, 0, 30); /* Martin Ettl, Nov 12 2012 */
(Haskell)
a008588 = (* 6)
a008588_list = [0, 6 ..]  -- Reinhard Zumkeller, Nov 10 2013

Crossrefs

Essentially the same as A008458.

Cf. A016921, A016933, A016945, A016957, A016969, A138591.

Cf. A044102 (subsequence).

Sequence in context: A126798 A175130 A008458 * A078596 A187389 A085129

Adjacent sequences: A008585 A008586 A008587 * A008589 A008590 A008591

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved