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%I #23 Sep 08 2022 08:45:58
%S 1,19,53,103,169,251,349,463,593,739,901,1079,1273,1483,1709,1951,
%T 2209,2483,2773,3079,3401,3739,4093,4463,4849,5251,5669,6103,6553,
%U 7019,7501,7999,8513,9043,9589,10151,10729,11323,11933,12559,13201,13859,14533
%N a(n) = 8*n^2 - 6*n - 1.
%C Sequence found by reading the line from 1, in the direction 1, 19, ..., in the square spiral whose vertices are the triangular numbers A000217.
%H Vincenzo Librandi, <a href="/A194431/b194431.txt">Table of n, a(n) for n = 1..10000</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 - 16*x + x^2) / (x-1)^3. - _R. J. Mathar_, Sep 06 2011
%t Table[8n^2-6n-1,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{1,19,53},50] (* _Harvey P. Dale_, May 29 2021 *)
%o (Magma) [8*n^2 - 6*n - 1: n in [1..50]]; _Vincenzo Librandi_, Sep 07 2011
%o (PARI) a(n)=8*n^2-6*n-1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A014634, A051870, A069129, A139098, A194268.
%K nonn,easy
%O 1,2
%A _Omar E. Pol_, Sep 05 2011
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