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%I #14 Aug 02 2023 14:38:11
%S 1,3,6,10,26,170,7226,13053770,42600227803226,
%T 453694852221687377444001770,
%U 51459754733114686962148583993443846186613037940783226,662026589298079856793872781777756720070052610825509991367405555066143474558289627235647952526950580741770
%N Related to expression as an alternating sum of k-th powers.
%C For n>=3 we have a(n+1) = (1/4)*(a(n)+2)^2 - a(n).
%H E. Lemoine, <a href="https://gallica.bnf.fr/ark:/12148/bpt6k201185m/f76.vertical">Sur la décomposition d'un nombre en ses carrés maxima</a>, Assoc. Française pour L'Avancement des Sciences (1896), 73-77.
%t a[1]=1; a[2]=3; a[3]=6; a[n_]:=(1/4)(a[n-1]+2)^2 - a[n-1]; Array[a,12] (* _Stefano Spezia_, Jul 12 2023 *)
%K nonn,easy
%O 1,2
%A _Jeffrey Shallit_, Jul 12 2023
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