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%I #35 Sep 08 2022 08:45:39
%S 0,8,48,120,224,360,528,728,960,1224,1520,1848,2208,2600,3024,3480,
%T 3968,4488,5040,5624,6240,6888,7568,8280,9024,9800,10608,11448,12320,
%U 13224,14160,15128,16128,17160,18224,19320,20448,21608,22800,24024,25280,26568
%N Eight times hexagonal numbers: 8*n*(2*n-1).
%C Equals Engel expansion of cosh(1/2), except first member (see A067239).
%C Also sequence found by reading the line from 0, in the direction 0, 8, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Sep 18 2011
%C a(n) = the sum of the edges of a rectangular prism having edges 2*(n-1)*n, n^2-(n-1)^2 and n^2 + (n-1)^2. - _J. M. Bergot_, Apr 24 2014
%H Ivan Panchenko, <a href="/A152750/b152750.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 16n^2 - 8n = A000384(n)*8 = A002939(n)*4 = A085250(n)*2.
%F a(n) = A067239(n), for n>0.
%F a(n) = a(n-1)+32*n-24 (with a(0)=0). - _Vincenzo Librandi_, Nov 26 2010
%F From _Colin Barker_, Sep 25 2016: (Start)
%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>2.
%F G.f.: 8*x*(1+3*x) / (1-x)^3.
%F (End)
%F Sum_{n>=1} 1/a(n) = log(2)/4. - _Vaclav Kotesovec_, Sep 25 2016
%p A152750:=n->8*n*(2*n-1); seq(A152750(n), n=0..50); # _Wesley Ivan Hurt_, Jun 09 2014
%t Table[8*n*(2*n - 1), {n, 0, 50}] (* _Wesley Ivan Hurt_, Jun 09 2014 *)
%o (Magma) [ 8*n*(2*n-1) : n in [0..50] ]; // _Wesley Ivan Hurt_, Jun 09 2014
%o (PARI) concat(0, Vec(8*x*(1+3*x)/(1-x)^3 + O(x^50))) \\ _Colin Barker_, Sep 25 2016
%Y Cf. A000384, A002939, A067239, A085250.
%K easy,nonn
%O 0,2
%A _Omar E. Pol_, Dec 12 2008
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