A132754 a(n) = n*(n + 23)/2.
0, 12, 25, 39, 54, 70, 87, 105, 124, 144, 165, 187, 210, 234, 259, 285, 312, 340, 369, 399, 430, 462, 495, 529, 564, 600, 637, 675, 714, 754, 795, 837, 880, 924, 969, 1015, 1062, 1110, 1159, 1209, 1260, 1312, 1365, 1419, 1474, 1530
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Mathematica
Table[n (n + 23)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 12, 25}, 50] (* Harvey P. Dale, Jun 21 2011 *) -
PARI
a(n)=n*(n+23)/2 \\ Charles R Greathouse IV, Jun 16 2017
Formula
a(n) = n*(n + 23)/2.
Let f(n,i,a) = Sum_{k=0..n-i} (binomial(n,k)*Stirling1(n-k,i)*Product_{j=0..k-1} (-a-j)), then a(n) = -f(n,n-1,12), for n>=1. - Milan Janjic, Dec 20 2008
a(n) = n + a(n-1) + 11, with a(0)=0. - Vincenzo Librandi, Aug 03 2010
a(0)=0, a(1)=12, a(2)=25, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jun 21 2011
a(n) = 12*n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013
From Amiram Eldar, Jan 10 2021: (Start)
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/23 - 3825136961/61573632120. (End)
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(11*x - 12)/(x-1)^3.
E.g.f.: exp(x)*x*(24 + x)/2.
a(n) = A132765(n)/2. (End)