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
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).
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved