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%I #35 Sep 08 2022 08:45:58
%S 0,2,5,9,15,21,30,38,50,60,75,87,105,119,140,156,180,198,225,245,275,
%T 297,330,354,390,416,455,483,525,555,600,632,680,714,765,801,855,893,
%U 950,990,1050,1092,1155,1199,1265,1311,1380,1428,1500,1550,1625,1677
%N Vertex number of a square spiral whose edges have length A195013.
%C Zero together with the partial partial sums of A195013.
%C Second bisection is 2, 9, 21, 38, 60, 87, 119, ...: A005476. - _Omar E. Pol_, Sep 25 2011
%C Number of pairs (x,y) with even x in {0,...,n}, odd y in {0,...,3n}, and x<y. - _Clark Kimberling_, Jul 02 2012
%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) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
%F G.f.: f(x)/g(x), where f(x) = 2*x + 3*x^2 and g(x) = (1+x)^2 * (1-x)^3. - _Clark Kimberling_, Jul 02 2012
%F a(n) = (10*n^2 + 18*n + 3 + (2*n - 3)*(-1)^n)/16. - _Luce ETIENNE_, Aug 11 2014
%t LinearRecurrence[{1,2,-2,-1,1},{0,2,5,9,15},60] (* _Harvey P. Dale_, May 20 2019 *)
%o (Magma) [(10*n^2 + 18*n + 3 + (2*n - 3)*(-1)^n)/16 : n in [0..50]]; // _Vincenzo Librandi_, Oct 26 2014
%Y Cf. A005476, A028895, A195013, A195020.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Sep 09 2011
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