%I
%S 1,11,33,67,113,171,241,323,417,523,641,771,913,1067,1233,1411,1601,
%T 1803,2017,2243,2481,2731,2993,3267,3553,3851,4161,4483,4817,5163,
%U 5521,5891,6273,6667,7073,7491,7921,8363,8817,9283,9761,10251,10753,11267
%N a(n) = 6*n^2 + 4*n + 1.
%C The old definition of this sequence was "Generalized polygonal numbers".
%C Column T(n,4) of A080853.
%C Sequence found by reading the line from 1, in the direction 1, 11,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318.  _Omar E. Pol_, Sep 08 2011
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,1).
%F G.f.: (C(3, 0)+(C(5, 2)2)*x+C(3, 2)*x^2)/(1x)^3 = (1+8*x+3*x^2)/(1x)^3.
%F E.g.f.: (1 + 10*x + 6*x^2)*exp(x).  _Vincenzo Librandi_, Apr 29 2016
%F a(n) = C(4, 0) + C(4, 1)n + C(4, 2)n^2.
%F a(n) = A186424(2*n).
%F a(n) = 12*n+a(n1)2 with n>0, a(0)=1.  _Vincenzo Librandi_, Aug 08 2010
%F a(n) = (n+1)*A000384(n+1)  n*A000384(n).  _Bruno Berselli_, Dec 10 2012
%t Table[6 n^2 + 4 n + 1, {n, 0, 50}] (* _Vincenzo Librandi_, Apr 29 2016 *)
%o (PARI) a(n)=6*n^2+4*n+1 \\ _Charles R Greathouse IV_, Oct 07 2015
%o (MAGMA) [6*n^2+4*n+1: n in [0..50]]; // _Vincenzo Librandi_, Apr 29 2016
%Y Subsequence of A186424.
%Y Cf. A000384, A001318, A033579, A033581.
%Y Cf. A220083 for a list of numbers of the form n*P(s,n)(n1)*P(s,n1), where P(s,n) is the nth polygonal number with s sides.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Feb 23 2003
%E Definition replaced with the closed form by _Bruno Berselli_, Dec 10 2012
