Search: id:A129556 Results 1-1 of 1 results found. %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, Centered Pentagonal Number. %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 Search completed in 0.001 seconds