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%I #14 Jan 02 2024 08:54:03
%S 1,8,92,1093,13021,155156,1848848,22031017,262523353,3128249216,
%T 37276467236,444189357613,5292995824117,63071760531788,
%U 751568130557336,8955745806156241,106717381543317553,1271652832713654392
%N Indices of 7-gonal numbers which are also centered 7-gonal numbers.
%C Numbers X such that 140*X^2-84*X-7 is a square.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13, -13, 1).
%F a(n+2)=12*a(n+1)-a(n)-3 ; a(n+1)=6*a(n)-1.5+0.5*(140*a(n)^2-84*a(n)-7)^0.5
%F G.f.: -x*(1-5*x+x^2)/(-1+x)/(1-12*x+x^2). - _R. J. Mathar_, Nov 14 2007
%F a(1)=1, a(2)=8, a(3)=92, a(n)=13*a(n-1)-13*a(n-2)+a(n-3). - _Harvey P. Dale_, Mar 24 2013
%t LinearRecurrence[{13,-13,1},{1,8,92},30] (* _Harvey P. Dale_, Mar 24 2013 *)
%Y Cf. A128919.
%K nonn
%O 1,2
%A _Richard Choulet_, Oct 16 2007
%E More terms from _Paolo P. Lava_, Jul 08 2008
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