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%I #48 Jan 16 2023 08:53:19
%S 0,1,14,29,56,85,126,169,224,281,350,421,504,589,686,785,896,1009,
%T 1134,1261,1400,1541,1694,1849,2016,2185,2366,2549,2744,2941,3150,
%U 3361,3584,3809,4046,4285,4536,4789,5054,5321,5600,5881,6174,6469,6776,7085,7406
%N Concentric 14-gonal numbers.
%C Also concentric tetradecagonal numbers or concentric tetrakaidecagonal numbers. Also sequence found by reading the line from 0, in the direction 0, 14, ..., and the same line from 1, in the direction 1, 29, ..., in the square spiral whose vertices are the generalized enneagonal numbers A118277. Main axis, perpendicular to A024966 in the same spiral.
%C Partial sums of A113801. - _Reinhard Zumkeller_, Jan 07 2012
%H Vincenzo Librandi, <a href="/A195145/b195145.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F G.f.: -x*(1+12*x+x^2) / ( (1+x)*(x-1)^3 ). - _R. J. Mathar_, Sep 18 2011
%F From _Vincenzo Librandi_, Sep 27 2011: (Start)
%F a(n) = (14*n^2 + 5*(-1)^n - 5)/4;
%F a(n) = a(-n) = -a(n-1) + 7*n^2 - 7*n + 1. (End)
%F Sum_{n>=1} 1/a(n) = Pi^2/84 + tan(sqrt(5/7)*Pi/2)*Pi/(2*sqrt(35)). - _Amiram Eldar_, Jan 16 2023
%t LinearRecurrence[{2, 0, -2, 1}, {0, 1, 14, 29}, 50] (* _Amiram Eldar_, Jan 16 2023 *)
%o (Magma) [(14*n^2+5*(-1)^n-5)/4: n in [0..50]]; // _Vincenzo Librandi_, Sep 27 2011
%o (Haskell)
%o a195145 n = a195145_list !! n
%o a195145_list = scanl (+) 0 a113801_list
%o -- _Reinhard Zumkeller_, Jan 07 2012
%Y A144555 and A195314 interleaved.
%Y Cf. A024966, A032527, A032528, A077221, A113801, A195045, A195046, A195142, A195143, A195146, A195147, A195148, A195149.
%Y Column 14 of A195040. - _Omar E. Pol_, Sep 28 2011
%K nonn,easy
%O 0,3
%A _Omar E. Pol_, Sep 17 2011
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