A098140 - OEIS

%I #48 Feb 10 2023 10:51:29

%S 0,1,63,186,370,615,921,1288,1716,2205,2755,3366,4038,4771,5565,6420,

%T 7336,8313,9351,10450,11610,12831,14113,15456,16860,18325,19851,21438,

%U 23086,24795,26565,28396,30288,32241,34255,36330,38466

%N 63-gonal numbers: a(n) = n*(61*n - 59)/2.

%H Vincenzo Librandi, <a href="/A098140/b098140.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

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

%F a(n) = n*(61*n - 59)/2.

%F G.f.: x*(1 + 60*x)/(1-x)^3. - _Bruno Berselli_, Feb 04 2011

%F a(0)=0, a(1)=1, a(2)=63, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Jun 09 2011

%F E.g.f.: exp(x)*(x + 61*x^2/2). - _Nikolaos Pantelidis_, Feb 10 2023

%t Table[n(61n - 59)/2, {n, 0, 50}] (* _Stefan Steinerberger_, Feb 28 2006 *)

%t LinearRecurrence[{3,-3,1},{0,1,63},50] (* _Harvey P. Dale_, Jun 09 2011 *)

%t CoefficientList[Series[x (1 + 60 x) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 16 2017 *)

%o (PARI) a(n)=n*(61*n-59)/2 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Magma) [(61*n^2-59*n)/2: n in [0..40]]; // _Vincenzo Librandi_, Aug 16 2017

%K nonn,easy

%O 0,3

%A _Parthasarathy Nambi_, Oct 25 2004

%E More terms from _Stefan Steinerberger_, Feb 28 2006

%E Offset corrected by _Eric Rowland_, Aug 15 2017