Search: id:A028872
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%I A028872
%S A028872 1,6,13,22,33,46,61,78,97,118,141,166,193,222,253,286,321,358,397,
%T A028872 438,481,526,573,622,673,726,781,838,897,958,1021,1086,1153,1222,
%U A028872 1293,1366,1441,1518,1597,1678,1761,1846,1933,2022,2113,2206,2301
%N A028872 n^2 - 3.
%C A028872 Number of edges in the join of two star graphs, each of order n, S_n 
               * S_n - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 
               07 2002
%C A028872 Sequence allows us to find X values of the equation: X^3 + (X - 3)^2 
               + X - 6 = Y^2. To prove that X = n^2 + 4n + 1: Y^2 = X^3 + (X - 3)^2 
               + X - 6 = X^3 + X^2 - 5X + 3 = (X + 3)(X^2 - 2X + 1) = (X + 3)*(X 
               - 1)^2 it means: X = 1 or (X + 3) must be a perfect square, so X 
               = k^2 - 3 with k>=2. we can put: k = n + 2, which gives: X = n^2 
               + 4n + 1 and Y = (n + 2)(n^2 + 4n). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), 
               Nov 29 2007
%C A028872 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 29 2009: 
               (Start)
%C A028872 Let C = 2 + sqrt(3) = 3.732...; and 1/C = .267...; then a(n) =
%C A028872 (n - 2 + C) * (n - 2 + 1/C). Example: a(5) = 46 = (5 + 3.732...)*(5 + 
               .267...). (End)
%C A028872 Except for the first term, a(n)=2*n+a(n-1)+3 (with a(1)=6) [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Nov 07 2009]
%H A028872 P. De Geest, <a href="http://www.worldofnumbers.com/consemor.htm">Palindromic 
               Quasipronics of the form n(n+x)</a>
%H A028872 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Near-SquarePrime.html">Near-Square Prime</a>
%F A028872 O.g.f.: x^2*(-1-3*x+2*x^2)/(-1+x)^3. a(n) = 3a(n-1)-3a(n-2)+a(n-3). - 
               R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2008
%F A028872 Equals binomial transform of [1, 5, 2, 0, 0, 0,...] - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Apr 30 2008
%F A028872 a(n)=2*n+a(n-1)+1 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 29 2009]
%e A028872 For n=2, a(2)=2*2+1+1=6; n=3, a(3)=2*3+6+1=13; n=4, a(4)=2*4+13+1=22 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 29 2009]
%p A028872 with(combinat, fibonacci):seq(fibonacci(3, i)-4,i=2..48); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008
%t A028872 lst={};Do[AppendTo[lst,n^2-3],{n,6!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Jan 27 2009]
%t A028872 s = 1; lst = {s}; Do[s += n; AppendTo[lst, s], {n, 5, 100, 2}]; lst [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
%o A028872 sage: [lucas_number1(3,n,3) for n in xrange(2,50)] - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jul 03 2008
%Y A028872 Cf. A117950, A132411, A132414, A002522.
%Y A028872 Sequence in context: A056115 A101247 A072212 this_sequence A049718 A036707 
               A054311
%Y A028872 Adjacent sequences: A028869 A028870 A028871 this_sequence A028873 A028874 
               A028875
%K A028872 nonn,new
%O A028872 2,2
%A A028872 Patrick De Geest (pdg(AT)worldofnumbers.com)

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