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A008133 a(n) = floor(n/3)*floor((n+1)/3). 4

%I #35 Sep 08 2022 08:44:35

%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

%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_

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)