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A246172 a(n) = (n^2+9*n-8)/2.

%I A246172 #29 Feb 25 2023 05:23:39
%S A246172 1,7,14,22,31,41,52,64,77,91,106,122,139,157,176,196,217,239,262,286,
%T A246172 311,337,364,392,421,451,482,514,547,581,616,652,689,727,766,806,847,
%U A246172 889,932,976,1021,1067,1114,1162,1211,1261,1312,1364,1417,1471
%N A246172 a(n) = (n^2+9*n-8)/2.
%C A246172 a(n) - 7*(n-1) is a triangular number. Sequence gives positive x values solving the Diophantine equation y^2 - 8*x = 113. - _Bruno Berselli_, Aug 27 2014
%H A246172 Vincenzo Librandi, <a href="/A246172/b246172.txt">Table of n, a(n) for n = 1..1000</a>
%H A246172 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A246172 G.f.: x*(1+4*x-4*x^2)/(1-x)^3.
%F A246172 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) = 2*a(n-1)-a(n-2)+1.
%F A246172 a(n+1) - a(n) = n + 5. - _Jacques ALARDET_, Aug 04 2015
%F A246172 Sum_{n>=1} 1/a(n) = 4919/8008 + 2*Pi*tan(sqrt(113)*Pi/2)/sqrt(113). - _Amiram Eldar_, Feb 25 2023
%t A246172 Table[(n^2 + 9 n - 8)/2, {n, 1, 60}]
%o A246172 (Magma) [(n^2+9*n-8)/2: n in [1..60]];
%o A246172 (Sage) [(n^2+9*n-8)/2 for n in (1..60)] # _Bruno Berselli_, Aug 27 2014
%o A246172 (PARI) a(n)=(n^2+9*n-8)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%K A246172 nonn,easy
%O A246172 1,2
%A A246172 _Vincenzo Librandi_, Aug 24 2014