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%I #25 Apr 14 2023 15:48:36
%S 1,16,47,94,157,236,331,442,569,712,871,1046,1237,1444,1667,1906,2161,
%T 2432,2719,3022,3341,3676,4027,4394,4777,5176,5591,6022,6469,6932,
%U 7411,7906,8417,8944,9487,10046,10621,11212,11819,12442,13081,13736,14407
%N a(n) = 8*n^2 + 7*n + 1.
%C Sequence found by reading the line from 1, in the direction 1, 16,..., in the square spiral whose vertices are the triangular numbers A000217.
%H Vincenzo Librandi, <a href="/A194268/b194268.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F a(0)=1, a(1)=16, a(2)=47, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - _Harvey P. Dale_, Apr 06 2014
%p A194268:=n->8*n^2+7*n+1: seq(A194268(n), n=0..50); # _Wesley Ivan Hurt_, Jul 15 2014
%t Table[8n^2+7n+1,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,16,47},50] (* _Harvey P. Dale_, Apr 06 2014 *)
%o (Magma) [8*n^2 +7*n + 1: n in [0..50]]; // _Vincenzo Librandi_, Sep 07 2011
%o (PARI) a(n)=8*n^2+7*n+1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A014634, A069129, A051870, A139098, A194431.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Sep 05 2011
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