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A081587 Third row of Pascal-(1,4,1) array A081579.

%I A081587 #21 Sep 05 2025 00:58:19
%S A081587 1,11,46,106,191,301,436,596,781,991,1226,1486,1771,2081,2416,2776,
%T A081587 3161,3571,4006,4466,4951,5461,5996,6556,7141,7751,8386,9046,9731,
%U A081587 10441,11176,11936,12721,13531,14366,15226,16111,17021,17956,18916,19901,20911,21946
%N A081587 Third row of Pascal-(1,4,1) array A081579.
%H A081587 G. C. Greubel, <a href="/A081587/b081587.txt">Table of n, a(n) for n = 0..1000</a>
%H A081587 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A081587 a(n) = (2 - 5*n + 25*n^2)/2.
%F A081587 G.f.: (1+4*x)^2/(1-x)^3.
%F A081587 a(n) = a(n-1) + 25*n - 15 with a(0)=1. - _Vincenzo Librandi_, Aug 08 2010
%F A081587 E.g.f.: (1/2)*(2 + 20*x + 25*x^2)*exp(x). - _G. C. Greubel_, May 26 2021
%e A081587 a(1) = 25*1+1-15 = 11.
%e A081587 a(2) = 25*2+11-15 = 46.
%e A081587 a(3) = 25*3+46-15 = 106.
%t A081587 ((10*Range[0,40]-1)^2 +7)/8 (* _G. C. Greubel_, May 26 2021 *)
%o A081587 (PARI) a(n)=5*n*(5*n-1)/2+1 \\ _Charles R Greathouse IV_, Jun 16 2017
%o A081587 (Magma) [(2-5*n+25*n^2)/2: n in [0..50]]; // _G. C. Greubel_, May 26 2021
%o A081587 (Sage) [((10*n-1)^2 +7)/8 for n in (0..40)] # _G. C. Greubel_, May 26 2021
%Y A081587 Cf. A016861, A081588.
%K A081587 easy,nonn,changed
%O A081587 0,2
%A A081587 _Paul Barry_, Mar 23 2003