A081587 - OEIS

%I #17 Sep 08 2022 08:45:09

%S 1,11,46,106,191,301,436,596,781,991,1226,1486,1771,2081,2416,2776,

%T 3161,3571,4006,4466,4951,5461,5996,6556,7141,7751,8386,9046,9731,

%U 10441,11176,11936,12721,13531,14366,15226,16111,17021,17956,18916,19901

%N Third row of Pascal-(1,4,1) array A081579.

%H G. C. Greubel, <a href="/A081587/b081587.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) = (2 - 5*n + 25*n^2)/2.

%F G.f.: (1+4*x)^2/(1-x)^3.

%F a(n) = a(n-1) + 25*n - 15 with a(0)=1. - _Vincenzo Librandi_, Aug 08 2010

%F E.g.f.: (1/2)*(2 + 20*x + 25*x^2)*exp(x). - _G. C. Greubel_, May 26 2021

%e a(1)=25*1+1-15=11; a(2)=25*2+11-15=46; a(3)=25*3+46-15=106.

%t ((10*Range[0,40]-1)^2 +7)/8 (* _G. C. Greubel_, May 26 2021 *)

%o (PARI) a(n)=5*n*(5*n-1)/2+1 \\ _Charles R Greathouse IV_, Jun 16 2017

%o (Magma) [(2-5*n+25*n^2)/2: n in [0..50]]; // G. C. Greubel, May 26 2021

%o (Sage) [((10*n-1)^2 +7)/8 for n in (0..40)] # _G. C. Greubel_, May 26 2021

%Y Cf. A016861, A081588.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 23 2003