%I A129556
%S A129556 0,2,21,95,816,3626,31005,137711,1177392,5229410,44709909,198579887,
%T A129556 1697799168,7540806314,64471658493,286352060063,2448225223584,
%U A129556 10873837476098,92968086837717,412919472031679,3530339074609680
%N A129556 Numbers n such that centered pentagonal number A005891(n) = (5n^2+5n+2)/
               2 is a perfect square.
%C A129556 Corresponding numbers k>0 such that k^2 is a centered pentagonal number 
               are listed in A129557(n) = {1, 4, 34, 151, 1291, 5734, 49024, ...}.
%H A129556 Eric Weisstein, Link to a section of The World of Mathematics, <a href="http:/
               /mathworld.wolfram.com/CenteredPentagonalNumber.html">Centered Pentagonal 
               Number</a>.
%F A129556 For n>=5, a(n) = 38*a(n-2) - a(n-4) + 18 [From Max Alekseyev (maxale(AT)gmail.com), 
               May 08 2009]
%p A129556 A005891 := proc(n) (5*n^2+5*n+2)/2 ; end: n := 0 : while true do if issqr(A005891(n)) 
               then print(n) ; fi ; n := n+1 ; od : - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jun 06 2007
%t A129556 Do[ f=(5n^2+5n+2)/2; If[ IntegerQ[ Sqrt[f] ], Print[n] ], {n,1,40000} 
               ]
%Y A129556 Cf. A005891 = Centered pentagonal numbers: (5n^2+5n+2)/2. Cf. A129557 
               = numbers k>0 such that k^2 is a centered pentagonal number.
%Y A129556 Sequence in context: A075681 A034520 A111128 this_sequence A077209 A068045 
               A079840
%Y A129556 Adjacent sequences: A129553 A129554 A129555 this_sequence A129557 A129558 
               A129559
%K A129556 nonn
%O A129556 1,2
%A A129556 Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 20 2007
%E A129556 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 06 2007
%E A129556 Formula and further terms from Max Alekseyev (maxale(AT)gmail.com), May 
               08 2009