Search: id:A125651
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%I A125651
%S A125651 1,3,24,147,864,5043,29400,171363,998784,5821347,33929304,197754483,
%T A125651 1152597600,6717831123,39154389144,228208503747,1330096633344,
%U A125651 7752371296323,45184131144600,263352415571283,1534930362283104
%N A125651 Numbers k such that A125650(k) is a perfect square.
%C A125651 Corresponding numbers m such that m^2 = A125650(a(n)) are listed in A125652.
%C A125651 3 divides a(n) for n>1. For n>1 a(n) = 3*A001108(n-1), where A001108(k) 
               = {0, 1, 8, 49, 288, 1681, ...}, A001108(k)-th triangular number 
               is a square. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 19 
               2007
%F A125651 For n>1, a(n+2) = 6*a(n+1) - a(n) + 6.
%F A125651 For n>1, a(n) = ((3+2*sqrt(2))^(n-1) + (3-2*sqrt(2))^(n-1))*3/4 - 3/2.
%F A125651 a(2k) = 3*A002315(n)^2; a(2k+1) = 6*A001542(n)^2.
%F A125651 a(n) = 3*A001108(n-1) for n>1. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Jan 19 2007
%e A125651 a(2)=3 because A125650(3)=9=3^2; a(3)=24 because A125650(24)=81=9^2.
%Y A125651 Cf. A125650, A125652.
%Y A125651 Cf. A001108.
%Y A125651 Sequence in context: A069515 A056350 A056344 this_sequence A043017 A003443 
               A119581
%Y A125651 Adjacent sequences: A125648 A125649 A125650 this_sequence A125652 A125653 
               A125654
%K A125651 nonn
%O A125651 1,2
%A A125651 Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 29 2006
%E A125651 Edited by Max Alekseyev (maxale(AT)gmail.com), Jan 11 2007

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