%I A134582
%S A134582 0,12,32,60,96,140,192,252,320,396,480,572,672,780,896,1020,1152,1292,
%T A134582 1440,1596,1760,1932,2112,2300,2496,2700,2912,3132,3360,3596,3840,4092,
%U A134582 4352,4620,4896,5180,5472,5772,6080,6396,6720,7052,7392,7740,8096,8460
%N A134582 (2*n)^2-4.
%H A134582 R. E. Borcherds, E. Freitag, R. Weissauer, <a href="http://arXiv.org/
               abs/math/9805132">A Siegel cusp form of degree 12 and weight 12</
               a>, arXiv:math/9805132, row A_2 page 6.
%F A134582 O.g.f.: 4-12/(-1+x)^2-8/(-1+x)^3 . a(n) = 4*A005563(n-1). - R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Jan 24 2008
%F A134582 a(n)=8*n+a(n-1)-4 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 12 2009]
%e A134582 Geometry: denote castle by x.
%e A134582 From
%e A134582 xx
%e A134582 xx
%e A134582 we get (2*1)^2-4=0
%e A134582 From
%e A134582 ******
%e A134582 ******
%e A134582 **xx**
%e A134582 **xx**
%e A134582 ******
%e A134582 ******
%e A134582 we get (2*3)^2-4=32
%e A134582 From (chess)
%e A134582 ********
%e A134582 ********
%e A134582 ********
%e A134582 ***xx***
%e A134582 ***xx***
%e A134582 ********
%e A134582 ********
%e A134582 ********
%e A134582 we get 8*8-4=60 [(2*4)^2-4=60]
%e A134582 etc...
%e A134582 For n=2, a(2)=8*2+0-4=12; n=3, a(3)=8*3+12-4=32; n=4, a(4)=8*4+32-4=60 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
%p A134582 seq((2*k)^2-4, k=1..46);
%t A134582 lst={};Do[AppendTo[lst, (2*n)^2-4], {n, 1, 5!}];lst...and/or... s=-4;
               lst={};Do[s+=n+1;AppendTo[lst, s], {n, 3, 6!, 8}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
%Y A134582 Sequence in context: A071336 A051519 A166959 this_sequence A081268 A068381 
               A143238
%Y A134582 Adjacent sequences: A134579 A134580 A134581 this_sequence A134583 A134584 
               A134585
%K A134582 nonn,new
%O A134582 1,2
%A A134582 Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 23 2008