%I #34 Sep 15 2024 19:05:42

%S 0,7,29,66,118,185,267,364,476,603,745,902,1074,1261,1463,1680,1912,

%T 2159,2421,2698,2990,3297,3619,3956,4308,4675,5057,5454,5866,6293,

%U 6735,7192,7664,8151,8653,9170,9702,10249,10811,11388,11980,12587,13209,13846,14498

%N a(n) = n*(15*n - 1)/2.

%H G. C. Greubel, <a href="/A022272/b022272.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) = 15*n + a(n-1) - 8 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 04 2010

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

%F G.f.: x*(7 + 8*x)/(1 - x)^3.

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

%F From _Bruno Berselli_, Mar 31 2015: (Start)

%F a(n) = A022273(-n).

%F a(n) + a(-n) = A064761(n). (End)

%F a(n) = A000217(8*n-1) - A000217(7*n-1). - _Bruno Berselli_, Oct 17 2016

%F E.g.f.: (x/2)*(15*x + 14)*exp(x). - _G. C. Greubel_, Aug 23 2017

%t Table[n (15 n - 1)/2, {n, 0, 40}] (* _Bruno Berselli_, Mar 12 2015 *)

%t CoefficientList[Series[x (7 + 8 x) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 31 2015 *)

%t LinearRecurrence[{3,-3,1},{0,7,29},50] (* _Harvey P. Dale_, Sep 15 2024 *)

%o (Magma) [n*(15*n - 1)/2: n in [0..45]]; // _Vincenzo Librandi_, Mar 31 20125

%o (PARI) a(n)=n*(15*n-1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A000217, A022273, A064761.

%Y Cf. similar sequences listed in A022288.

%K nonn,easy,changed

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Mar 31 2015