A152995 - OEIS

%I #32 May 31 2024 14:16:20

%S 0,2,22,60,116,190,282,392,520,666,830,1012,1212,1430,1666,1920,2192,

%T 2482,2790,3116,3460,3822,4202,4600,5016,5450,5902,6372,6860,7366,

%U 7890,8432,8992,9570,10166,10780,11412,12062,12730,13416,14120

%N Twice 11-gonal numbers: a(n) = n*(9*n-7).

%H G. C. Greubel, <a href="/A152995/b152995.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) = 9*n^2 - 7*n = A051682(n)*2.

%F a(n) = a(n-1) + 18*n - 16 (with a(0)=0). - _Vincenzo Librandi_, Nov 27 2010

%F a(0)=0, a(1)=2, a(2)=22, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Nov 02 2011

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

%F G.f.: 2*x*(1+8*x)/(1-x)^3.

%F E.g.f.: x*(2+9*x)*exp(x). (End)

%p seq(n*(9*n-7), n=0..50); # _G. C. Greubel_, Sep 01 2019

%t Table[n(9n-7),{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{0,2,22},40] (* _Harvey P. Dale_, Nov 02 2011 *)

%t 2*PolygonalNumber[11,Range[0,40]] (* _Harvey P. Dale_, May 31 2024 *)

%o (Magma) [n*(9*n-7): n in [0..50]];

%o (PARI) a(n)=n*(9*n-7) \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Sage) [n*(9*n-7) for n in (0..50)] # _G. C. Greubel_, Sep 01 2019

%o (GAP) List([0..50], n-> n*(9*n-7)); # _G. C. Greubel_, Sep 01 2019

%Y Cf. A051682 (11-gonal numbers).

%Y Cf. A226488.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, Dec 22 2008