This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A008810 a(n) = ceiling(n^2/3). 22

%I

%S 0,1,2,3,6,9,12,17,22,27,34,41,48,57,66,75,86,97,108,121,134,147,162,

%T 177,192,209,226,243,262,281,300,321,342,363,386,409,432,457,482,507,

%U 534,561,588,617,646,675,706,737,768,801,834,867,902,937,972,1009,1046

%N a(n) = ceiling(n^2/3).

%C a(n+1) is the number of 3-tuples (w,x,y) having all terms in {0,...,n} and 3w=2x+y. - _Clark Kimberling_, Jun 04 2012

%C a(A008585(n)) = A033428(n). - _Reinhard Zumkeller_, Dec 20 2012

%C a(n) is also the number of L-shape (3 boxes polyomino) packing into n X n square. See illustration in links. - _Kival Ngaokrajang_, Nov 10 2013

%D J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, number of red blocks in Fig 2.5.

%H Reinhard Zumkeller, <a href="/A008810/b008810.txt">Table of n, a(n) for n = 0..10000</a>

%H S. Lafortune, A. Ramani, B. Grammaticos, Y. Ohta and K.M. Tamizhmani, <a href="http://arXiv.org/abs/nlin.SI/0104020">Blending two discrete integrability criteria: ...</a>, arXiv:nlin/0104020 [nlin.SI], 2001.

%H Kival Ngaokrajang, <a href="/A008810/a008810.pdf">Illustration of initial terms</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).

%F Euler transform of length 6 sequence [ 2, 0, 2, 0, 0, -1]. - _Michael Somos_, Aug 03 2006

%F a(-n) = a(n) = ceiling(n^2/3).

%F G.f.: x*(1+x^3)/((1-x)^2*(1-x^3)) = x*(1-x^6)/((1-x)*(1-x^3))^2.

%F a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5), n>4. - _Harvey P. Dale_, Jun 20 2011

%F 9*a(n) = 4 +3*n^2 -2*A099837(n+3). - _R. J. Mathar_, May 02 2013

%F a(n) = n^2 - 2*A000212(n). - _Wesley Ivan Hurt_, Jul 07 2013

%p seq(ceil(n^2/3), n=0..60); # _G. C. Greubel_, Sep 12 2019

%t Ceiling[Range[0,60]^2/3] (* _Vladimir Joseph Stephan Orlovsky_, Mar 15 2011 *)

%t LinearRecurrence[{2,-1,1,-2,1},{0,1,2,3,6},60] (* _Harvey P. Dale_, Jun 20 2011 *)

%o (PARI) a(n)=ceil(n^2/3) /* _Michael Somos_, Aug 03 2006 */

%o a008810 = ceiling . (/ 3) . fromInteger . a000290

%o a008810_list = [0,1,2,3,6] ++ zipWith5

%o (\u v w x y -> 2 * u - v + w - 2 * x + y)

%o (drop 4 a008810_list) (drop 3 a008810_list) (drop 2 a008810_list)

%o (tail a008810_list) a008810_list

%o -- _Reinhard Zumkeller_, Dec 20 2012

%o (MAGMA) [Ceiling(n^2/3): n in [0..60]]; // _G. C. Greubel_, Sep 12 2019

%o (Sage) [ceil(n^2/3) for n in (0..60)] # _G. C. Greubel_, Sep 12 2019

%Y A056105(n)=a(3n-1). A056109(n)=a(3n+1). - _Michael Somos_, Aug 03 2006

%Y Cf. A000290.

%Y Cf. Expansions of the form (1+x^m)/((1-x)^2*(1-x^m)): A000290 (m=1), A000982 (m=2), this sequence (m=3), A008811 (m=4), A008812 (m=5), A008813 (m=6), A008814 (m=7), A008815 (m=8), A008816 (m=9), A008817 (m=10).

%K nonn,easy,nice

%O 0,3

%A _N. J. A. Sloane_

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.

Last modified December 6 21:48 EST 2019. Contains 329809 sequences. (Running on oeis4.)