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%I #13 Oct 24 2023 13:57:54
%S 0,9,324,11025,374544,12723489,432224100,14682895929,498786237504,
%T 16944049179225,575598885856164,19553418069930369,664240615491776400,
%U 22564627508650467249,766533094678624110084,26039560591564569275625
%N Perfect squares one less than a triangular number.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (35, -35, 1).
%F a(n) = A164055(n)-1.
%F a(n) = A072221(n)*(A072221(n)+1)/2 - 1.
%F a(n) = 35*a(n-1) -35*a(n-2) +a(n-3) = 9*A001110(n-1). G.f.: 9*x^2*(1+x)/((1-x)*(x^2-34*x+1)). [_R. J. Mathar_, Oct 21 2009]
%e 324=18^2 is a perfect square and 325=A000217(25) is a triangular number. Therefore 324 is in this sequence.
%t LinearRecurrence[{35,-35,1},{0,9,324},20] (* _Harvey P. Dale_, Oct 24 2023 *)
%K nonn
%O 1,2
%A _Tanya Khovanova_ & Alexey Radul, Aug 09 2009
%E Comments turned into formulas. - _R. J. Mathar_, Oct 21 2009
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