A132755 a(n) = n*(n + 25)/2.
0, 13, 27, 42, 58, 75, 93, 112, 132, 153, 175, 198, 222, 247, 273, 300, 328, 357, 387, 418, 450, 483, 517, 552, 588, 625, 663, 702, 742, 783, 825, 868, 912, 957, 1003, 1050, 1098, 1147, 1197, 1248, 1300, 1353, 1407, 1462, 1518, 1575
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[n*(n + 25)/2 : n in [0..50]]; // Wesley Ivan Hurt, Jan 23 2017
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Mathematica
Table[(n(n+25))/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,13,27},50] (* Harvey P. Dale, Aug 09 2014 *) -
PARI
a(n)=n*(n+25)/2 \\ Charles R Greathouse IV, Jun 17 2017
Formula
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, 13), for n>=1. - Milan Janjic, Dec 20 2008
a(n) = n + a(n-1) + 12 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
a(n) = 13*n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013
a(0)=0, a(1)=13, a(2)=27; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Aug 09 2014
From Amiram Eldar, Jan 10 2021: (Start)
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/25 - 19081066231/334639305000. (End)
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(12*x - 13)/(x-1)^3.
E.g.f.: exp(x)*x*(26 + x)/2.
a(n) = A132767(n)/2. (End)