|
%I #16 Aug 29 2016 00:16:26
%S 0,10,50,120,220,350,510,700,920,1170,1450,1760,2100,2470,2870,3300,
%T 3760,4250,4770,5320,5900,6510,7150,7820,8520,9250,10010,10800,11620,
%U 12470,13350,14260,15200,16170,17170,18200,19260,20350
%N 10 times pentagonal numbers: a(n) = 5*n*(3*n-1).
%H G. C. Greubel, <a href="/A153780/b153780.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) = 15*n^2 - 5*n = 10*A000326(n) = 5*A049450(n) = 2*A152734(n).
%F a(n) = 30*n + a(n-1) - 20 for n>0, a(0) = 0. - _Vincenzo Librandi_, Aug 03 2010
%F G.f.: 10*x*(1+2*x)/(1-x)^3. - _Colin Barker_, Feb 14 2012
%F From _G. C. Greubel_, Aug 28 2016: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F E.g.f.: 5*x*(2 + 3*x)*exp(x). (End)
%t Table[5*n*(3*n - 1), {n,0,25}] (* or *) LinearRecurrence[{3,-3,1},{0,10,50},25] (* _G. C. Greubel_, Aug 28 2016 *)
%o (PARI) a(n) = 5*n*(3*n-1); \\ _Michel Marcus_, Aug 28 2016
%Y Cf. A000326, A049450, A152734, A152996, A153449.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Jan 01 2009
|
