%I #37 Sep 08 2022 08:44:46

%S 0,9,37,84,150,235,339,462,604,765,945,1144,1362,1599,1855,2130,2424,

%T 2737,3069,3420,3790,4179,4587,5014,5460,5925,6409,6912,7434,7975,

%U 8535,9114,9712,10329,10965,11620,12294,12987,13699,14430,15180,15949,16737,17544,18370

%N a(n) = n*(19*n - 1)/2.

%H G. C. Greubel, <a href="/A022276/b022276.txt">Table of n, a(n) for n = 0..5000</a>

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

%F a(n) = 19*n + a(n-1) - 10 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 04 2010

%F From _Vincenzo Librandi_, Mar 31 2015: (Start)

%F G.f.: x*(9 + 10*x)/(1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. (End)

%F a(n) = A022277(-n). - _Bruno Berselli_, Apr 01 2015

%F a(n) = A000217(10*n-1) - A000217(9*n-1). - _Bruno Berselli_, Oct 17 2016

%F E.g.f.: (x/2)*(19*x + 18)*exp(x). - _G. C. Greubel_, Aug 23 2017

%t Table[n (19 n - 1)/2, {n, 0, 40}] (* _Bruno Berselli_, Mar 12 2015 *)

%t CoefficientList[Series[x (9 + 10 x) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 31 2015 *)

%t LinearRecurrence[{3,-3,1},{0,9,37},50] (* _Harvey P. Dale_, Jul 25 2021 *)

%o (Magma) [n*(19*n - 1)/2: n in [0..45]]; // _Vincenzo Librandi_, Mar 31 2015

%o (PARI) a(n)=n*(19*n-1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A000217, A022277.

%Y Cf. similar sequences listed in A022288.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Mar 31 2015