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A239796 a(n) = 7*n^2 + 2*n - 15.

%I A239796 #56 Sep 08 2022 08:46:07
%S A239796 -6,17,54,105,170,249,342,449,570,705,854,1017,1194,1385,1590,1809,
%T A239796 2042,2289,2550,2825,3114,3417,3734,4065,4410,4769,5142,5529,5930,
%U A239796 6345,6774,7217,7674,8145,8630,9129,9642,10169,10710,11265,11834,12417,13014,13625,14250,14889,15542,16209,16890
%N A239796 a(n) = 7*n^2 + 2*n - 15.
%C A239796 Follows the integer values from 1 on the parabola: 7*n^2 + 2*n - 15.
%C A239796 Real roots: (-1 +- sqrt(106))/7. - _Wesley Ivan Hurt_, Mar 26 2014
%C A239796 The first in the family of parabolas of the form: prime(k+3)*n^2 + prime(k)*n - prime(k+1)*prime(k+2), where k >= 1 (k=1 gives a(n)). - _Wesley Ivan Hurt_, Mar 26 2014
%H A239796 Vincenzo Librandi, <a href="/A239796/b239796.txt">Table of n, a(n) for n = 1..1000</a>
%H A239796 Vi Hart, <a href="https://www.youtube.com/watch?v=v-pyuaThp-c">Doodling in Math Class: Connecting Dots</a> (2012) [Video]
%H A239796 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A239796 a(n) = n * A017005(n) - 15. - _Wesley Ivan Hurt_, Mar 26 2014
%F A239796 G.f.: -x*(6 - 35*x + 15*x^2)/(1 - x)^3. - _Bruno Berselli_, Mar 27 2014
%e A239796 For n=3, a(3) = 7*3^2 + 2*3 - 15 = 54; for n=6, a(6) = 7*6^2 + 2*6 - 15 = 249.
%p A239796 A239796:=n->7*n^2 +2*n - 15; seq(A239796(n), n=1..50); # _Wesley Ivan Hurt_, Mar 26 2014
%t A239796 Table[7 n^2 + 2 n - 15, {n, 50}] (* _Wesley Ivan Hurt_, Mar 26 2014 *)
%t A239796 CoefficientList[Series[(6 - 35 x + 15 x^2)/(x - 1)^3, {x, 0, 50}], x] (* _Vincenzo Librandi_, Mar 29 2014 *)
%o A239796 (Magma) [7*n^2+2*n-15: n in [1..50]]; // _Bruno Berselli_, Mar 27 2014
%o A239796 (PARI) a(n)=7*n^2 + 2*n - 15 \\ _Charles R Greathouse IV_, Jan 21 2016
%K A239796 sign,easy
%O A239796 1,1
%A A239796 _Katherine Guo_, Mar 26 2014