%I #15 Sep 08 2022 08:45:40
%S 1,9,26,55,99,161,244,351,485,649,846,1079,1351,1665,2024,2431,2889,
%T 3401,3970,4599,5291,6049,6876,7775,8749,9801,10934,12151,13455,14849,
%U 16336,17919,19601,21385,23274,25271,27379,29601,31940,34399,36981
%N (n+3)^2*n/2 + 1.
%C 8*a(n) is the y value of a solution (x, y) to the Diophantine equation 2*x^3+12*x^2 = y^2. The corresponding x value is A152811(n+1).
%H Vincenzo Librandi, <a href="/A154560/b154560.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: (1+5*x-4*x^2+x^3)/(1-x)^4.
%F a(n) = A058794(n)/2.
%F a(n) = A117560(n+2) - n - 1.
%F a(2*n) = A144129(n+1).
%F a(2*n-1) = A141530(n+1). a(n) = -a(-n-4). - _Bruno Berselli_, Sep 05 2011
%e a(5) = (5+3)^2*5/2+1 = 64*5/2+1 = 161.
%o (PARI) {for(n=0,40,print1((n+3)^2*n/2+1,","))}
%o (Magma) [(n+3)^2*n/2 + 1: n in [0..50]]; // _Vincenzo Librandi_, Sep 06 2011
%Y Cf. A058794 (row 3 of A007754), A117560 (n*(n^2-1)/2-1), A144129 (4*n^3-3*n), A141530, A152811 (2*(n^2+2*n-2)).
%K nonn,easy
%O 0,2
%A _Klaus Brockhaus_, Jan 12 2009