%I #32 Sep 08 2022 08:44:46

%S 0,8,31,69,122,190,273,371,484,612,755,913,1086,1274,1477,1695,1928,

%T 2176,2439,2717,3010,3318,3641,3979,4332,4700,5083,5481,5894,6322,

%U 6765,7223,7696,8184,8687,9205,9738,10286,10849,11427,12020,12628,13251,13889

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

%H G. C. Greubel, <a href="/A022273/b022273.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) = A110449(n, 7) for n>6.

%F a(n) = 15*n + a(n-1) - 7 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 04 2010

%F G.f.: x*(8+7*x)/(1-x)^3. - _Vincenzo Librandi_, Mar 31 2015

%F a(n) = 3*a(n-1) - 3*a(n-2) - a(n-3) for n>2. - _Vincenzo Librandi_, Mar 31 2015

%F a(n) = A022272(-n). - _Bruno Berselli_, Mar 31 2015

%F a(n) + a(-n) = A064761(n). - _Bruno Berselli_, Mar 31 2015

%F a(n) = A000217(8*n) - A000217(7*n). - _Bruno Berselli_, Oct 13 2016

%F E.g.f.: (x/2)*(15*x + 16)*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 (8 + 7 x) / (1 - x)^3, {x, 0, 40}], x]; (* _Vincenzo Librandi_, Mar 31 2015 *)

%o (Magma) [n*(15*n + 1)/2: n in [0..45]]; // _Vincenzo Librandi_, Mar 31 2015

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

%Y Cf. A022272, A064761, A110449.

%Y Cf. similar sequences listed in A022289.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Mar 31 2015