Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #37 Sep 21 2024 17:32:55
%S 0,0,0,1,1,2,4,4,6,9,9,12,16,16,20,25,25,30,36,36,42,49,49,56,64,64,
%T 72,81,81,90,100,100,110,121,121,132,144,144,156,169,169,182,196,196,
%U 210,225,225,240,256,256,272,289,289,306,324,324,342,361,361,380,400,400,420,441,441,462,484,484,506
%N a(n) = floor(n/3)*floor((n+1)/3).
%C Oblong numbers and squares are subsequences: a(A016789(n))=A002378(n); a(A008585(n))=a(A016777(n))=A000290(n). - _Reinhard Zumkeller_, Oct 09 2011
%H Vincenzo Librandi, <a href="/A008133/b008133.txt">Table of n, a(n) for n = 0..10000</a>
%H V. Baltic, <a href="http://yujor.fon.bg.ac.rs/index.php/yujor/article/view/395">Applications of the finite state automata for counting restricted permutations and variations</a>, Yugoslav Journal of Operations Research, 22 (2012), Number 2, 183-198 ; DOI: 10.2298/YJOR120211023B. - From _N. J. A. Sloane_, Jan 02 2013
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1)
%F Partial sums of A087509. a(n+1)=sum{j=0..n, sum{k=0..j, if (mod(jk, 3)=2, 1, 0) }}. - _Paul Barry_, Sep 14 2003
%F Empirical g.f.: -x^3*(x^2+1) / ((x-1)^3*(x^2+x+1)^2). - _Colin Barker_, Mar 31 2013
%t Table[Floor[n/3]Floor[(n+1)/3],{n,0,100}] (* or *) LinearRecurrence[{1,0,2,-2,0,-1,1},{0,0,0,1,1,2,4},100] (* _Harvey P. Dale_, Sep 21 2024 *)
%o (Magma) [Floor(n/3)*Floor((n+1)/3): n in [0..60]]; // _Vincenzo Librandi_, Aug 20 2011
%o (Haskell)
%o a008133 n = a008133_list !! n
%o a008133_list = zipWith (*) (tail ts) ts where ts = map (`div` 3) [0..]
%o -- _Reinhard Zumkeller_, Oct 09 2011
%o (PARI) a(n) = floor(n/3)*floor((n+1)/3); /* _Joerg Arndt_, Mar 31 2013 */
%Y Cf. A008217.
%K nonn,easy
%O 0,6
%A _N. J. A. Sloane_