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A139098 8n^2. 19

%I

%S 0,8,32,72,128,200,288,392,512,648,800,968,1152,1352,1568,1800,2048,

%T 2312,2592,2888,3200,3528,3872,4232,4608,5000,5408,5832,6272,6728,

%U 7200,7688,8192,8712,9248,9800,10368,10952,11552,12168,12800

%N 8n^2.

%C Opposite numbers to the centered 16-gonal numbers (A069129) in the square spiral whose vertices are the triangular numbers (A000217).

%C 8 times the squares. - _Omar E. Pol_, Dec 09 2008

%C a(n-1) is the molecular topological index of the n-wheel graph W_n. - _Eric W. Weisstein_, Jul 11 2011

%C An n * n pandiagonal magic square has a(n) orientations. - _Kausthub Gudipati_, Sep 15, 2011

%C Area of a square with diagonal 4n. - _Wesley Ivan Hurt_, Jun 19 2014

%C Sum of all the parts in the partitions of 4n into exactly two parts. - _Wesley Ivan Hurt_, Jul 23 2014

%H Vincenzo Librandi, <a href="/A139098/b139098.txt">Table of n, a(n) for n = 0..800</a>

%H Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = A000290(n)*8. - _Omar E. Pol_, Dec 09 2008

%F a(n) = A001105(n)*4 = A016742(n)*2. - _Omar E. Pol_, Dec 13 2008

%F G.f.: -8*x*(1+x) / (x-1)^3 . - _R. J. Mathar_, Nov 27 2015

%p A139098:=n->8*n^2; seq(A139098(n), n=0..50); # _Wesley Ivan Hurt_, Jun 19 2014

%t s=0;lst={s};Do[s+=n++ +8;AppendTo[lst, s], {n, 0, 8!, 16}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 16 2008 *)

%t 8 Range[0, 50]^2 (* _Wesley Ivan Hurt_, Jun 19 2014 *)

%o (MAGMA) [8*n^2: n in [0..50]]; // _Vincenzo Librandi_, Apr 26 2011

%Y Cf. A000217, A000290, A016766, A033582, A069129, A001105, A016742.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, Apr 25 2008

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Last modified December 8 06:50 EST 2016. Contains 278902 sequences.