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.
%I A210982 #51 Aug 21 2022 04:19:01
%S A210982 0,1,8,12,26,33,54,64,92,105,140,156,198,217,266,288,344,369,432,460,
%T A210982 530,561,638,672,756,793,884,924,1022,1065,1170,1216,1328,1377,1496,
%U A210982 1548,1674,1729,1862,1920,2060,2121,2268,2332,2486,2553,2714,2784,2952,3025,3200,3276,3458,3537,3726
%N A210982 Zero together with A126264 and positive terms of A051624 interleaved.
%C A210982 Vertex number of a square spiral similar to A195162.
%C A210982 This is the case k=5 of the formula b(n,k) = ( 2*(k+5)*n^2+2*(k+3)*n-(k+1)+(2*(k-1)*n+k+1)*(-1)^n )/16. Sequences of the same family: A093025 (k=-1, with an initial 0), A210977 (k=0), A006578 (k=1), A210978 (k=2), A181995 (k=3, with one 0 only), A210981 (k=4). - _Luce ETIENNE_, Oct 30 2014
%H A210982 G. C. Greubel, <a href="/A210982/b210982.txt">Table of n, a(n) for n = 0..5000</a>
%H A210982 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A210982 G.f.: x*(1+7*x+2*x^2) / ( (1+x)^2*(1-x)^3 ). - _R. J. Mathar_, Aug 07 2012
%F A210982 a(n) = (10*n^2 +8*n -3 +(4*n+3)*(-1)^n)/8. - _Luce ETIENNE_, Oct 14 2014
%F A210982 E.g.f.: (1/8)*((10*x^3 + 18*x -3)*exp(x) - (4*x - 3)*exp(-x)). - _G. C. Greubel_, Aug 23 2017
%F A210982 Sum_{n>=1} 1/a(n) = 5/9 + (sqrt(1-2/sqrt(5))/6 + sqrt(1+2/sqrt(5))/8)*Pi + 7*log(phi)*sqrt(5)/24 - 5*log(5)/48, where phi is the golden ratio (A001622). - _Amiram Eldar_, Aug 21 2022
%t A210982 Table[(10*n^2 + 8*n - 3 + (4*n + 3)*(-1)^n)/8, {n, 0, 50}] (* _G. C. Greubel_, Aug 23 2017 *)
%o A210982 (Magma) [(10*n^2+8*n-3+(4*n+3)*(-1)^n )/8: n in [0..60]]; // _Vincenzo Librandi_, Oct 31 2014
%o A210982 (PARI) my(x='x+O('x^50)); Vec(x*(1+7*x+2*x^2)/((1+x)^2*(1-x)^3)) \\ _G. C. Greubel_, Aug 23 2017
%Y A210982 Members of this family are A093005, A210977, A006578, A210978, A181995, A210981, this sequence.
%Y A210982 Cf. A001622, A051624, A126264, A195162.
%K A210982 nonn,easy
%O A210982 0,3
%A A210982 _Omar E. Pol_, Aug 03 2012