A152997 - OEIS

%I #29 Sep 08 2022 08:45:39

%S 0,2,26,72,140,230,342,476,632,810,1010,1232,1476,1742,2030,2340,2672,

%T 3026,3402,3800,4220,4662,5126,5612,6120,6650,7202,7776,8372,8990,

%U 9630,10292,10976,11682,12410,13160,13932,14726,15542,16380,17240,18122,19026,19952,20900,21870,22862,23876

%N Twice 13-gonal numbers: a(n) = n*(11*n - 9).

%H G. C. Greubel, <a href="/A152997/b152997.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 11*n^2 - 9*n = A051865(n)*2.

%F a(n) = a(n-1) + 22*n - 20 (with a(0)=0). - _Vincenzo Librandi_, Nov 27 2010

%F From _G. C. Greubel_, Sep 01 2019: (Start)

%F G.f.: 2*x*(1 + 10*x)/(1-x)^3.

%F E.g.f.: x*(2 + 11*x)*exp(x). (End)

%p seq(n*(11*n-9), n=0..50); # _G. C. Greubel_, Sep 01 2019

%t Table[n*(11*n-9), {n,0,50}] (* _G. C. Greubel_, Sep 01 2019 *)

%o (Magma) [n*(11*n-9): n in [0..50]];

%o (PARI) a(n)=n*(11*n-9) \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Sage) [n*(11*n-9) for n in (0..50)] # _G. C. Greubel_, Sep 01 2019

%o (GAP) List([0..50], n-> n*(11*n-9)); # _G. C. Greubel_, Sep 01 2019

%Y Cf. A051865 (13-gonal numbers).

%Y Cf. numbers of the form n*(n*k - k + 4))/2 listed in A226488 (this sequence is the case k=22). - _Bruno Berselli_, Jun 10 2013

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, Dec 22 2008

%E Terms a(39) onward added by _G. C. Greubel_, Sep 01 2019