%I A135405
%S A135405 0,1,8,8,17,19,30,34,47,53,68,76,93,103,122,134,155,169,192,208,233,251,
%T A135405 278,298,327,349,380,404,437,463,498,526,563,593,632,664,705,739,782,
%U A135405 818,863,901,948,988,1037,1079,1130,1174,1227,1273,1328,1376,1433,1483
%N A135405 Sequence where the sum of each pair of consecutive elements is a square. 
               This covers squares of all consecutively increasing integers with 
               the exception of 2.
%C A135405 a(n)=(n+2)*(n+1)/2+2*(-1)^n
%F A135405 O.g.f.: -x*(1+6*x-8*x^2+3*x^3)/((-1+x)^3*(1+x)) = -3-1/(-1+x)^3+2/(1+x). 
               a(n)= A000217(n+1)+2*(-1)^n if n>0. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Dec 12 2007
%e A135405 a(1)=1 because 0 + 1 = 1^2
%e A135405 a(2)=8 because 1 + 8 = 9 = 3^2
%e A135405 a(3)=8 because 8 + 8 =16 = 4^2
%t A135405 a=1; lst={0, a}; Do[a=n^2-a; AppendTo[lst, a], {n, 3, 5!}]; lst [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 17 2008]
%Y A135405 Sequence in context: A112439 A022091 A145909 this_sequence A006784 A061156 
               A109049
%Y A135405 Adjacent sequences: A135402 A135403 A135404 this_sequence A135406 A135407 
               A135408
%K A135405 nonn
%O A135405 0,3
%A A135405 Alexander R. Povolotsky (pevnev(AT)juno.com), Dec 11 2007, Apr 02 2008
%E A135405 More terms and Mathematica program Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Dec 17 2008