%I #18 Sep 08 2022 08:45:09
%S 1,22,73,154,265,406,577,778,1009,1270,1561,1882,2233,2614,3025,3466,
%T 3937,4438,4969,5530,6121,6742,7393,8074,8785,9526,10297,11098,11929,
%U 12790,13681,14602,15553,16534,17545,18586,19657,20758,21889,23050
%N 15*n^2 + 6*n + 1.
%C The old definition of this sequence was "Generalized polygonal numbers".
%C Column T(n,6) of A080853.
%H Vincenzo Librandi, <a href="/A080861/b080861.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = C(6,0) + C(6,1)*n + C(6,2)*n^2.
%F G.f.: (C(5,0)+(C(7,2)-2)*x+C(5,2)*x^2)/(1-x)^3 = (1+19*x+10*x^2)/(1-x)^3.
%t CoefficientList[Series[(1 + 19 x + 10 x^2) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 05 2013 *)
%t LinearRecurrence[{3, -3, 1}, {1, 22, 73}, 40] (* _Harvey P. Dale_, Sep 28 2019 *)
%o (Magma) [15*n^2 + 6*n + 1 : n in [0..40]]; // _Vincenzo Librandi_, Aug 05 2013
%o (PARI) a(n)=15*n^2+6*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%K nonn,easy
%O 0,2
%A _Paul Barry_, Feb 23 2003
%E Definition replaced with the closed form by _Bruno Berselli_, Jan 16 2013