A154591 a(n) = 2*n^2 + 18*n + 7.
27, 51, 79, 111, 147, 187, 231, 279, 331, 387, 447, 511, 579, 651, 727, 807, 891, 979, 1071, 1167, 1267, 1371, 1479, 1591, 1707, 1827, 1951, 2079, 2211, 2347, 2487, 2631, 2779, 2931, 3087, 3247, 3411, 3579, 3751, 3927, 4107, 4291, 4479, 4671, 4867, 5067, 5271
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
-
Magma
I:=[27, 51, 79]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 22 2012
-
Mathematica
LinearRecurrence[{3, -3, 1}, {27, 51, 79}, 50] (* Vincenzo Librandi, Feb 22 2012 *) -
PARI
for(n=1, 40, print1(2*n^2 + 18*n + 7", ")); \\ Vincenzo Librandi, Feb 22 2012
-
SageMath
[2*n^2+18*n+7 for n in range(1,51)] # G. C. Greubel, May 27 2024
Formula
G.f.: (9*x^2-6*x-7)/(x-1)^3. - Bruno Berselli, Dec 07 2011
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 22 2012
Sum_{n>=1} 1/a(n) = 1621/20097 + tan(sqrt(67)*Pi/2)*Pi/(2*sqrt(67)). - Amiram Eldar, Feb 25 2023
E.g.f.: (7 + 20*x + 2*x^2)*exp(x). - G. C. Greubel, May 27 2024
Comments