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%I #11 Sep 08 2022 08:45:09
%S 1,13,61,145,265,421,613,841,1105,1405,1741,2113,2521,2965,3445,3961,
%T 4513,5101,5725,6385,7081,7813,8581,9385,10225,11101,12013,12961,
%U 13945,14965,16021,17113,18241,19405,20605,21841,23113,24421,25765,27145
%N Third row of Pascal-(1,5,1) array A081580.
%H Vincenzo Librandi, <a href="/A081589/b081589.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) = 1-6*n+18*n^2.
%F G.f.: (1+5*x)^2/(1-x)^3.
%t CoefficientList[Series[(1 + 5 x)^2 / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 09 2013 *)
%o (Magma) [1-6*n+18*n^2: n in [0..40]]; // _Vincenzo Librandi_, Aug 09 2013
%o (PARI) a(n)=18*n^2-6*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A016921, A081590.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 23 2003
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