A153449 - OEIS

%I #21 Jun 17 2017 03:37:16

%S 0,11,55,132,242,385,561,770,1012,1287,1595,1936,2310,2717,3157,3630,

%T 4136,4675,5247,5852,6490,7161,7865,8602,9372,10175,11011,11880,12782,

%U 13717,14685,15686,16720,17787,18887,20020,21186,22385

%N 11 times pentagonal numbers: 11*n*(3n-1)/2.

%H Ivan Panchenko, <a href="/A153449/b153449.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) = (33*n^2 - 11*n)/2 = A000326(n)*11.

%F a(n) = 33*n + a(n-1) - 22 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010

%F G.f.: 11*x*(1+2*x)/(1-x)^3. - _Colin Barker_, Feb 21 2012

%F From _G. C. Greubel_, Aug 21 2016: (Start)

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

%F E.g.f.: (11/2)*x*(2 + 3*x)*exp(x). (End)

%t Table[11*n*(3n-1)/2, {n,0,25}] (* or *) LinearRecurrence[{3,-3,1},{0,11,55},25] (* _G. C. Greubel_, Aug 21 2016 *)

%o (PARI) a(n)=11*n*(3*n-1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A000326.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, Dec 26 2008