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%I #37 Sep 08 2022 08:44:46
%S 0,7,27,60,106,165,237,322,420,531,655,792,942,1105,1281,1470,1672,
%T 1887,2115,2356,2610,2877,3157,3450,3756,4075,4407,4752,5110,5481,
%U 5865,6262,6672,7095,7531,7980,8442,8917,9405,9906,10420,10947,11487,12040
%N a(n) = n*(13*n + 1)/2.
%H G. C. Greubel, <a href="/A022271/b022271.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, 6) for n>5.
%F a(n) = 13*n + a(n-1) - 6 with n>0, a(0)=0. - _Vincenzo Librandi_, Aug 04 2010
%F G.f.: x*(7+6*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) = A022270(-n). - _Bruno Berselli_, Mar 31 2015
%F a(n) = A000217(7*n) - A000217(6*n). - _Bruno Berselli_, Oct 13 2016
%F E.g.f.: (x/2)*(13*x + 14)*exp(x). - _G. C. Greubel_, Aug 23 2017
%t Table[n (13 n + 1)/2, {n, 0, 40}] (* _Vincenzo Librandi_, Mar 31 2015 *)
%t LinearRecurrence[{3,-3,1},{0,7,27},50] (* _Harvey P. Dale_, Jul 03 2022 *)
%o (Magma) [n*(13*n + 1)/2: n in [0..45]]; // _Vincenzo Librandi_, Mar 31 2015
%o (PARI) a(n)=n*(13*n+1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A022270, 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
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