Search: id:A102344
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%I A102344
%S A102344 2,7,97,1351,18817,262087,3650401,50843527,708158977,9863382151,
%T A102344 137379191137,1913445293767,26650854921601,371198523608647,
%U A102344 5170128475599457,72010600134783751,1002978273411373057
%N A102344 Numbers n such that the Diophantine equation (x+2)^3-x^3=2*n^2 has solutions.
%C A102344 n^2=3*(2*x+4)^2+16
%F A102344 a(n+2)=14*a(n+1)-a(n) for n>=2.
%F A102344 G.f.: x(2-21x+x^2)/(1-14x+x^2). a(n)=7*A007655(n+2)-97*A007655(n+1), 
               n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 11 2008]
%F A102344 a(n)=-2*sqrt(3)*{[7-4*sqrt(3)]^(n-1)-[7+4*sqrt(3)]^(n-1)}+(7/2)*{[7+4*sqrt(3)]^(n-1)+[7 
               -4*sqrt(3)]^(n-1)}+[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava 
               (ppl(AT)spl.at), Nov 25 2008]
%e A102344 The first examples are 2^3-0^3=2*2^2 ; 5^3-3^3=2*7^2 ; 57^3-55^3=2*97^2 
               ; 781^3-779^3=2*1351^2 ; 10865^3-10863^3=2*18817^2
%Y A102344 Sequence in context: A076740 A112290 A072059 this_sequence A087589 A002812 
               A102598
%Y A102344 Adjacent sequences: A102341 A102342 A102343 this_sequence A102345 A102346 
               A102347
%K A102344 easy,nonn
%O A102344 1,1
%A A102344 Richard Choulet (richardchoulet(AT)yahoo.fr), Sep 08 2008
%E A102344 Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 11 2008

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