cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A195158 Concentric 24-gonal numbers.

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%I A195158 #33 Jan 17 2023 09:23:53
%S A195158 0,1,24,49,96,145,216,289,384,481,600,721,864,1009,1176,1345,1536,
%T A195158 1729,1944,2161,2400,2641,2904,3169,3456,3745,4056,4369,4704,5041,
%U A195158 5400,5761,6144,6529,6936,7345,7776,8209,8664,9121,9600,10081,10584,11089
%N A195158 Concentric 24-gonal numbers.
%C A195158 Sequence found by reading the line from 0, in the direction 0, 24, ..., and the same line from 1, in the direction 1, 49, ..., in the square spiral whose vertices are the generalized tetradecagonal numbers A195818. Main axis, perpendicular to A049598 in the same spiral.
%H A195158 Vincenzo Librandi, <a href="/A195158/b195158.txt">Table of n, a(n) for n = 0..10000</a>
%H A195158 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A195158 a(n) = 6*n^2 + 5*((-1)^n-1)/2.
%F A195158 a(n) = -a(n-1) + A069190(n). - _Vincenzo Librandi_, Sep 30 2011
%F A195158 From _Colin Barker_, Sep 16 2012: (Start)
%F A195158 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F A195158 G.f.: x*(1+22*x+x^2)/((1-x)^3*(1+x)). (End)
%F A195158 Sum_{n>=1} 1/a(n) = Pi^2/144 + tan(sqrt(5/6)*Pi/2)*Pi/(4*sqrt(30)). - _Amiram Eldar_, Jan 17 2023
%t A195158 LinearRecurrence[{2,0,-2,1},{0,1,24,49},50] (* _Harvey P. Dale_, Jan 28 2021 *)
%o A195158 (Magma) [(12*n^2+5*(-1)^n-5)/2: n in [0..50]]; // _Vincenzo Librandi_, Sep 30 2011
%o A195158 (PARI) a(n)=6*n^2+5*((-1)^n-1)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A195158 Column 24 of A195040.
%Y A195158 Cf. A032527, A032528, A195143, A195149, A195058.
%K A195158 nonn,easy
%O A195158 0,3
%A A195158 _Omar E. Pol_, Sep 28 2011