A153169 a(n) = 4*n^2 + 12*n + 3.
19, 43, 75, 115, 163, 219, 283, 355, 435, 523, 619, 723, 835, 955, 1083, 1219, 1363, 1515, 1675, 1843, 2019, 2203, 2395, 2595, 2803, 3019, 3243, 3475, 3715, 3963, 4219, 4483, 4755, 5035, 5323, 5619, 5923, 6235, 6555, 6883, 7219, 7563, 7915, 8275, 8643, 9019, 9403
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
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Magma
I:=[19, 43, 75]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 25 2012
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Mathematica
LinearRecurrence[{3, -3, 1}, {19, 43, 75}, 50] (* Vincenzo Librandi, Feb 25 2012 *) -
PARI
for(n=1, 50, print1(4*n^2 + 12*n + 3", ")); \\ Vincenzo Librandi, Feb 25 2012
Formula
From Colin Barker, Jan 24 2012: (Start)
G.f.: x*(19 - 14*x + 3*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=19, a(2)=43, a(3)=75. (End)
Sum_{n>=1} 1/a(n) = -2/15 + tan(sqrt(3/2)*Pi)*Pi/(4*sqrt(6)). - Amiram Eldar, Mar 02 2023
From Elmo R. Oliveira, Jun 03 2025: (Start)
E.g.f.: -3 + (3 + 16*x + 4*x^2)*exp(x).
a(n) = A028878(2*n) for n >= 1. (End)
Extensions
Definition rewritten by Bruno Berselli, Jan 25 2012
Comments