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%I A022272 #34 Sep 15 2024 19:05:42
%S A022272 0,7,29,66,118,185,267,364,476,603,745,902,1074,1261,1463,1680,1912,
%T A022272 2159,2421,2698,2990,3297,3619,3956,4308,4675,5057,5454,5866,6293,
%U A022272 6735,7192,7664,8151,8653,9170,9702,10249,10811,11388,11980,12587,13209,13846,14498
%N A022272 a(n) = n*(15*n - 1)/2.
%H A022272 G. C. Greubel, <a href="/A022272/b022272.txt">Table of n, a(n) for n = 0..5000</a>
%H A022272 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A022272 a(n) = 15*n + a(n-1) - 8 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 04 2010
%F A022272 From _Vincenzo Librandi_, Mar 31 2015: (Start)
%F A022272 G.f.: x*(7 + 8*x)/(1 - x)^3.
%F A022272 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. (End)
%F A022272 From _Bruno Berselli_, Mar 31 2015: (Start)
%F A022272 a(n) = A022273(-n).
%F A022272 a(n) + a(-n) = A064761(n). (End)
%F A022272 a(n) = A000217(8*n-1) - A000217(7*n-1). - _Bruno Berselli_, Oct 17 2016
%F A022272 E.g.f.: (x/2)*(15*x + 14)*exp(x). - _G. C. Greubel_, Aug 23 2017
%t A022272 Table[n (15 n - 1)/2, {n, 0, 40}] (* _Bruno Berselli_, Mar 12 2015 *)
%t A022272 CoefficientList[Series[x (7 + 8 x) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 31 2015 *)
%t A022272 LinearRecurrence[{3,-3,1},{0,7,29},50] (* _Harvey P. Dale_, Sep 15 2024 *)
%o A022272 (Magma) [n*(15*n - 1)/2: n in [0..45]]; // _Vincenzo Librandi_, Mar 31 20125
%o A022272 (PARI) a(n)=n*(15*n-1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A022272 Cf. A000217, A022273, A064761.
%Y A022272 Cf. similar sequences listed in A022288.
%K A022272 nonn,easy
%O A022272 0,2
%A A022272 _N. J. A. Sloane_
%E A022272 More terms from _Vincenzo Librandi_, Mar 31 2015

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