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%I #60 Dec 31 2023 10:22:09
%S 1,9,23,43,69,101,139,183,233,289,351,419,493,573,659,751,849,953,
%T 1063,1179,1301,1429,1563,1703,1849,2001,2159,2323,2493,2669,2851,
%U 3039,3233,3433,3639,3851,4069,4293,4523,4759,5001,5249,5503,5763,6029,6301,6579
%N a(n) = 3*n^2 - n - 1.
%C Sequence's original Name was "First bisection of A135370."
%C The partial sums of this sequence give A081437. - _Leo Tavares_, Dec 26 2021
%H Vincenzo Librandi, <a href="/A144390/b144390.txt">Table of n, a(n) for n = 1..1000</a>
%H John Elias, <a href="/A144390/a144390.png">Illustration: Belted Hexagrams</a>
%H Leo Tavares, <a href="/A144390/a144390.jpg">Illustration: Bounded 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+1) = a(n) + 6*n + 2; see A016933.
%F G.f.: x*(1+6*x-x^2)/(1-x)^3. a(n) = A049450(n)-1. - _R. J. Mathar_, Oct 24 2008
%F a(-n) = A144391(n). - _Michael Somos_, Mar 27 2014
%F E.g.f.: (3*x^2 + 2*x -1)*exp(x) + 1. - _G. C. Greubel_, Jul 19 2017
%F From _Leo Tavares_, Dec 26 2021: (Start)
%F a(n) = A003215(n) - 2*A005408(n). See Bounded Hexagons illustration.
%F a(n) = A016754(n-1) - A002378(n-2). (End)
%F a(n) = A003154(n) - A049451(n-1). - _John Elias_, Dec 22 2022
%p A144390:=n->3*n^2-n-1; seq(A144390(n), n=1..50); # _Wesley Ivan Hurt_, Mar 26 2014
%t Table[3*n^2 -n -1 , {n,0,50}] (* _G. C. Greubel_, Jul 19 2017 *)
%o (Magma) [3*n^2-n-1: n in [1..60]]; // _Vincenzo Librandi_, Jun 14 2011
%o (PARI) a(n)=3*n^2-n-1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A016933, A049450, A144391.
%Y Cf. A003215, A005408, A016754, A002378.
%Y Cf. A081437 (partial sums).
%K nonn,easy
%O 1,2
%A _Paul Curtz_, Oct 02 2008
%E Edited by _R. J. Mathar_, Oct 24 2008
%E More terms from _Vladimir Joseph Stephan Orlovsky_, Oct 25 2008
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