A144391 a(n) = 3*n^2 + n - 1.
3, 13, 29, 51, 79, 113, 153, 199, 251, 309, 373, 443, 519, 601, 689, 783, 883, 989, 1101, 1219, 1343, 1473, 1609, 1751, 1899, 2053, 2213, 2379, 2551, 2729, 2913, 3103, 3299, 3501, 3709, 3923, 4143, 4369, 4601, 4839, 5083, 5333, 5589, 5851, 6119, 6393, 6673
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..3000
- Leo Tavares, Illustration: Cropped Hexagons
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[3*n^2+n-1: n in [1..50]]; // Vincenzo Librandi, May 06 2011
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Mathematica
Table[3 n^2 + n - 1, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {3, 13, 29}, 50] (* Harvey P. Dale, Sep 18 2016 *) -
PARI
a(n)=3*n^2+n-1 \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = A135370(2*n).
First differences: a(n+1) - a(n) = A016957(n).
From R. J. Mathar, Oct 24 2008: (Start)
G.f.: x*(3 + 4*x - x^2)/(1 - x)^3.
a(n) = A049451(n) - 1. (End)
E.g.f.: (3*x^2 + 4*x - 1)*exp(x) + 1. - G. C. Greubel, Jul 19 2017
a(n) = 1 + Sum_{i = n-1..2*n-1} 2*i. - Bruno Berselli, Feb 16 2018
a(n) = A003215(n) - (n+1)*2. - Leo Tavares, Jul 04 2021
Extensions
Edited by R. J. Mathar, Oct 24 2008
More terms from Vladimir Joseph Stephan Orlovsky, Mar 01 2009