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%I #34 Feb 11 2022 04:49:14
%S 1,29,85,169,281,421,589,785,1009,1261,1541,1849,2185,2549,2941,3361,
%T 3809,4285,4789,5321,5881,6469,7085,7729,8401,9101,9829,10585,11369,
%U 12181,13021,13889,14785,15709,16661,17641,18649,19685,20749,21841,22961,24109
%N Centered 28-gonal numbers.
%C Sequence found by reading the line from 1, in the direction 1, 29, ..., in the square spiral whose vertices are the generalized enneagonal numbers A118277. Semi-axis opposite to A144555 in the same spiral.
%H Vincenzo Librandi, <a href="/A195314/b195314.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 a(n) = 14*n^2 - 14*n + 1.
%F G.f.: -x*(1 + 26*x + x^2) / (x-1)^3. - _R. J. Mathar_, Sep 18 2011
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Oct 01 2011
%F Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(5/7)*Pi/2)/(2*sqrt(35)). - _Amiram Eldar_, Feb 11 2022
%t Table[14n^2-14n+1,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{1,29,85},50]
%o (Magma) [(14*n^2-14*n+1): n in [1..50]]; // _Vincenzo Librandi_, Sep 19 2011
%o (PARI) a(n)=14*n^2-14*n+1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Bisection of A195145.
%Y Cf. A003154, A069129, A069133, A069190, A195315, A195316, A195317, A195318.
%K nonn,easy
%O 1,2
%A _Omar E. Pol_, Sep 16 2011
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