Search: id:A028347
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%I A028347
%S A028347 0,5,12,21,32,45,60,77,96,117,140,165,192,221,252,285,320,
%T A028347 357,396,437,480,525,572,621,672,725,780,837,896,957,1020,
%U A028347 1085,1152,1221,1292,1365,1440,1517,1596,1677,1760,1845
%N A028347 n^2 - 4.
%C A028347 Sequence allows us to find X values of the equation: X^3 + 4*X^2 = Y^2. 
               To find Y values: b(n)=n*(n^2 - 4). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), 
               Nov 06 2007
%C A028347 Discriminants of binary forms x^2 + n*x*y + y^2 (for n>1) - Artur Jasinski 
               (grafix(AT)csl.pl), Apr 28 2008
%C A028347 Number of units of a(n) belongs to a periodic sequence: 0, 5, 2, 1, 2, 
               5, 0, 7, 6, 7. [From Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 
               04 2009]
%D A028347 A. Connes, Noncommutative Geometry, Academic Press, 1994, p. 35.
%H A028347 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A028347 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Near-SquarePrime.html">Near-Square Prime</a>
%F A028347 Except for initial term, denominators of wavelengths of hydrogen lines.
%F A028347 a(n+2)=n(n+4). G.f.(x)=x^3*(5-3*x)/(1-x)^3 - Barry E. Williams, Jun 16 
               2000, R. J. Mathar, Aug 06 2009
%F A028347 Except for the first term, a(n)=2*n+a(n-1)+3 (with a(1)=5) [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Nov 07 2009]
%p A028347 a:=n->sum(n,j=5..n): seq(a(n), n=4..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Feb 12 2007
%p A028347 with(combinat):seq(fibonacci(3, i)-5,i=2..43); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 20 2008
%p A028347 with(finance):seq(add(cashflows([k, k, 3], 0 ), k=1..n), n=0..45); # 
               [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
%t A028347 lst={};Do[AppendTo[lst, n^2-4], {n, 2, 6!}];lst [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Nov 06 2008]
%o A028347 (Other) SAGE: [lucas_number2(2,n,2) for n in xrange(2,44)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]
%Y A028347 a(n), n>=3, second column (used for the Balmer series of the hydrogen 
               atom) of triangle A120070.
%Y A028347 Cf. A005563, A046092, A001082, A002378, A036666, A062717.
%Y A028347 Sequence in context: A063559 A121291 A097984 this_sequence A038794 A131976 
               A074376
%Y A028347 Adjacent sequences: A028344 A028345 A028346 this_sequence A028348 A028349 
               A028350
%K A028347 nonn,new
%O A028347 2,2
%A A028347 N. J. A. Sloane (njas(AT)research.att.com).
%E A028347 Formula adapted to the offset by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Aug 06 2009

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