%I #30 Jan 11 2021 02:49:44
%S 0,16,33,51,70,90,111,133,156,180,205,231,258,286,315,345,376,408,441,
%T 475,510,546,583,621,660,700,741,783,826,870,915,961,1008,1056,1105,
%U 1155,1206,1258,1311,1365,1420,1476,1533,1591,1650
%N a(n) = n*(n + 31)/2.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F a(n) = n*(n+31)/2.
%F If we define f(n,i,r) = Sum_{k=0..n-i} binomial(n,k) * Stirling1(n-k,i) * Product_{j=0..k-1} (-r-j), then a(n) = -f(n,n-1,16) for n>=1. - _Milan Janjic_, Dec 20 2008
%F a(n) = n + a(n-1) + 15 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F a(0)=0, a(1)=16, a(2)=33; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Jun 21 2012
%F a(n) = 16*n - floor(n/2) + floor(n^2/2). - _Wesley Ivan Hurt_, Jun 15 2013
%F From _Amiram Eldar_, Jan 11 2021: (Start)
%F Sum_{n>=1} 1/a(n) = 2*A001008(31)/(31*A002805(31)) = 290774257297357/1119127534925400.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/31 - 7313175618421/159875362132200. (End)
%t Table[(n(n+31))/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,16,33},50] (* _Harvey P. Dale_, Jun 21 2012 *)
%o (PARI) a(n)=n*(n+31)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A000217, A001008, A002805, A056126.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Aug 28 2007