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%I #31 Sep 08 2022 08:45:28
%S 2,19,52,101,166,247,344,457,586,731,892,1069,1262,1471,1696,1937,
%T 2194,2467,2756,3061,3382,3719,4072,4441,4826,5227,5644,6077,6526,
%U 6991,7472,7969,8482,9011,9556,10117,10694,11287,11896,12521,13162,13819,14492,15181
%N a(n) = 8*n^2 - 7*n + 1.
%C Central terms of the triangle in A125199.
%C Sequence found by reading the line from 2, in the direction 2, 19, ..., in the square spiral whose vertices are the triangular numbers A000217. - _Omar E. Pol_, Sep 05 2011
%H Arkadiusz Wesolowski, <a href="/A125201/b125201.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 a(n) = 1 + A051870(n). - Omar E. Pol, Sep 05 2011
%F From _Arkadiusz Wesolowski_, Dec 25 2011: (Start)
%F a(1) = 2, a(n) = a(n-1) + 16*n - 15.
%F a(n) = 2*a(n-1) - a(n-2) + 16 with a(1) = 2 and a(2) = 19.
%F G.f.: (1 - x + 16*x^2)/(1 - x)^3. (End)
%t Table[8*n^2 - 7*n + 1, {n, 44}] (* _Arkadiusz Wesolowski_, Feb 15 2012 *)
%o (Magma) [8*n^2-7*n+1:n in [1..44]]; // _Vincenzo Librandi_, Dec 27 2010
%o (PARI) a(n)=8*n^2-7*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%K nonn,easy
%O 1,1
%A _Reinhard Zumkeller_, Nov 24 2006
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