A022279 - OEIS

%I #30 Jul 15 2018 13:53:56

%S 0,11,43,96,170,265,381,518,676,855,1055,1276,1518,1781,2065,2370,

%T 2696,3043,3411,3800,4210,4641,5093,5566,6060,6575,7111,7668,8246,

%U 8845,9465,10106,10768,11451,12155

%N a(n) = n*(21*n + 1)/2.

%H G. C. Greubel, <a href="/A022279/b022279.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) = 21*n + a(n-1) - 10 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 04 2010

%F a(0)=0, a(1)=11, a(2)=43; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, May 06 2014

%F a(n) = A000217(11*n) - A000217(10*n). - _Bruno Berselli_, Oct 13 2016

%F From _G. C. Greubel_, Aug 23 2017: (Start)

%F G.f.: x*(10*x + 11)/(1-x)^3.

%F E.g.f.: (x/2)*(21*x + 22)*exp(x). (End)

%t Table[n (21 n + 1)/2, {n, 0, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 07 2011 *)

%t LinearRecurrence[{3, -3, 1}, {0, 11, 43}, 40] (* _Harvey P. Dale_, May 06 2014 *)

%o (PARI) a(n)=n*(21*n+1)/2 \\ _Charles R Greathouse IV_, Jun 16 2017

%Y Cf. similar sequences listed in A022289.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_