A132758 a(n) = n*(n + 31)/2.
0, 16, 33, 51, 70, 90, 111, 133, 156, 180, 205, 231, 258, 286, 315, 345, 376, 408, 441, 475, 510, 546, 583, 621, 660, 700, 741, 783, 826, 870, 915, 961, 1008, 1056, 1105, 1155, 1206, 1258, 1311, 1365, 1420, 1476, 1533, 1591, 1650
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Mathematica
Table[(n(n+31))/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,16,33},50] (* Harvey P. Dale, Jun 21 2012 *) -
PARI
a(n)=n*(n+31)/2 \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = n*(n + 31)/2.
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
a(n) = n + a(n-1) + 15 for n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010
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
a(n) = 16*n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013
From Amiram Eldar, Jan 11 2021: (Start)
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/31 - 7313175618421/159875362132200. (End)
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(15*x - 16)/(x-1)^3.
E.g.f.: exp(x)*x*(32 + x)/2.
a(n) = A132773(n)/2. (End)