A132757 a(n) = n*(n+29)/2.
0, 15, 31, 48, 66, 85, 105, 126, 148, 171, 195, 220, 246, 273, 301, 330, 360, 391, 423, 456, 490, 525, 561, 598, 636, 675, 715, 756, 798, 841, 885, 930, 976, 1023, 1071, 1120, 1170, 1221, 1273, 1326, 1380, 1435, 1491, 1548, 1606, 1665
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Mathematica
i=-14;s=0;lst={};Do[s+=n+i;If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 29 2008 *) -
PARI
a(n)=n*(n+29)/2 \\ Charles R Greathouse IV, Jun 17 2017
Formula
If we define 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-1,15), for n >= 1. - Milan Janjic, Dec 20 2008
a(n) = n + a(n-1) + 14 with n > 0, a(0)=0. - Vincenzo Librandi, Aug 03 2010
From Colin Barker, Mar 18 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(15-14*x)/(1-x)^3. (End)
a(n) = 15*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)/29 - 236266661971/4824542665800. (End)
From Elmo R. Oliveira, Jan 12 2025: (Start)
E.g.f.: exp(x)*x*(30 + x)/2.
a(n) = A132771(n)/2. (End)