A144391 - OEIS

%I #46 Sep 08 2022 08:45:38

%S 3,13,29,51,79,113,153,199,251,309,373,443,519,601,689,783,883,989,

%T 1101,1219,1343,1473,1609,1751,1899,2053,2213,2379,2551,2729,2913,

%U 3103,3299,3501,3709,3923,4143,4369,4601,4839,5083,5333,5589,5851,6119,6393,6673

%N a(n) = 3*n^2 + n - 1.

%H Vincenzo Librandi, <a href="/A144391/b144391.txt">Table of n, a(n) for n = 1..3000</a>

%H Leo Tavares, <a href="/A144391/a144391.jpg">Illustration: Cropped Hexagons</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = A135370(2*n).

%F First differences: a(n+1) - a(n) = A016957(n).

%F a(n) - A144390(n) = 6*n + 4 = A005843(n).

%F From _R. J. Mathar_, Oct 24 2008: (Start)

%F G.f.: x*(3 + 4*x - x^2)/(1 - x)^3.

%F a(n) = A049451(n) - 1. (End)

%F E.g.f.: (3*x^2 + 4*x - 1)*exp(x) + 1. - _G. C. Greubel_, Jul 19 2017

%F a(n) = 1 + Sum_{i = n-1..2*n-1} 2*i. - _Bruno Berselli_, Feb 16 2018

%F a(n) = A003215(n) - (n+1)*2. - _Leo Tavares_, Jul 04 2021

%t Table[3 n^2 + n - 1, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {3, 13, 29}, 50] (* _Harvey P. Dale_, Sep 18 2016 *)

%o (Magma) [3*n^2+n-1: n in [1..50]]; // _Vincenzo Librandi_, May 06 2011

%o (PARI) a(n)=3*n^2+n-1 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A135370, A144390.

%K nonn,easy

%O 1,1

%A _Paul Curtz_, Oct 02 2008

%E Edited by _R. J. Mathar_, Oct 24 2008

%E More terms from _Vladimir Joseph Stephan Orlovsky_, Mar 01 2009