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%I #31 Sep 08 2022 08:45:02
%S 0,3,15,24,48,63,99,120,168,195,255,288,360,399,483,528,624,675,783,
%T 840,960,1023,1155,1224,1368,1443,1599,1680,1848,1935,2115,2208,2400,
%U 2499,2703,2808,3024,3135,3363,3480,3720,3843,4095,4224,4488,4623,4899,5040
%N Multiples of 3 that are one less than a perfect square.
%C Also, numbers of the form 9*m^2+6*m, m an integer. - _Jason Kimberley_, Nov 08 2012
%C k is in this list iff k+1 is in the support of A033684. - _Jason Kimberley_, Nov 13 2012
%H Jason Kimberley, <a href="/A057780/b057780.txt">Table of n, a(n) for n = 1..2001</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F a(n) = A001651(n)^2 - 1 = 3 * A001082(n).
%F G.f.: 3*x^2*(1+4*x+x^2) / ((1-x)^3*(1+x)^2). - _Colin Barker_, Nov 24 2012
%F From _Colin Barker_, Dec 26 2015: (Start)
%F a(n) = 3/8*(6*n^2-2*((-1)^n+3)*n+(-1)^n-1).
%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>5.
%F (End)
%t Select[3*Range[0,2000],IntegerQ[Sqrt[#+1]]&] (* or *) LinearRecurrence[ {1,2,-2,-1,1},{0,3,15,24,48},50] (* _Harvey P. Dale_, Sep 10 2019 *)
%o (Magma) a:=func<n|9*n^2+6*n>;[0]cat[a(n*m):m in[-1, 1],n in[1..24]]; // _Jason Kimberley_, Nov 09 2012
%o (PARI) concat(0, Vec(3*x^2*(1+4*x+x^2)/((1-x)^3*(1+x)^2) + O(x^100))) \\ _Colin Barker_, Dec 26 2015
%Y Numbers of the form 9n^2+kn, for integer n: A016766 (k=0), A132355 (k=2), A185039 (k=4), this sequence (k=6), A218864 (k=8). - _Jason Kimberley_, Nov 08 2012
%K nonn,easy
%O 1,2
%A Benjamin Geiger (benjamin_geiger(AT)yahoo.com), Nov 02 2000
%E Since this is a list, offset corrected to 1 by _Jason Kimberley_, Nov 09 2012
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