%I #29 Feb 25 2023 05:23:39

%S 1,7,14,22,31,41,52,64,77,91,106,122,139,157,176,196,217,239,262,286,

%T 311,337,364,392,421,451,482,514,547,581,616,652,689,727,766,806,847,

%U 889,932,976,1021,1067,1114,1162,1211,1261,1312,1364,1417,1471

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

%C 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 Vincenzo Librandi, <a href="/A246172/b246172.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

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

%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) = 2*a(n-1)-a(n-2)+1.

%F a(n+1) - a(n) = n + 5. - _Jacques ALARDET_, Aug 04 2015

%F Sum_{n>=1} 1/a(n) = 4919/8008 + 2*Pi*tan(sqrt(113)*Pi/2)/sqrt(113). - _Amiram Eldar_, Feb 25 2023

%t Table[(n^2 + 9 n - 8)/2, {n, 1, 60}]

%o (Magma) [(n^2+9*n-8)/2: n in [1..60]];

%o (Sage) [(n^2+9*n-8)/2 for n in (1..60)] # _Bruno Berselli_, Aug 27 2014

%o (PARI) a(n)=(n^2+9*n-8)/2 \\ _Charles R Greathouse IV_, Jun 17 2017

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Aug 24 2014