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 A142710 #17 Oct 26 2022 03:04:49
%S A142710 2,2,6,14,38,112,276,814,1998,5702,14226,39404,99908,270922,695106,
%T A142710 1859134,4807518,12748472,33128916,87394454,227792678,599050102,
%U A142710 1564242906,4106054164,10733283588,28143585362,73614464826,192899714414,504751433798,1322156172352
%N A142710 a(n) = A142585(n) + A142586(n).
%C A142710 Sum of the binomial and inverse binomial transforms of A014217.
%C A142710 Starting at a(1), the last digits form a period-4 sequence 2, 6, 4, 8.
%H A142710 G. C. Greubel, <a href="/A142710/b142710.txt">Table of n, a(n) for n = 0..1000</a>
%H A142710 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,7,-12,-11,16,-4).
%F A142710 a(n) = +2*a(n-1) +7*a(n-2) -12*a(n-3) -11*a(n-4) +16*a(n-5) -4*a(n-6), n>6. - _R. J. Mathar_, Jun 14 2010
%F A142710 G.f.: 2*(1-x-6*x^2+6*x^3+7*x^4-2*x^6)/((1-2*x)*(1+2*x)*(1+x-x^2)*(1-3*x+x^2)). - _Colin Barker_, Aug 13 2012
%F A142710 a(n) = (-1)^n*LucasL(n) + LucasL(2*n) - (1 + (-1)^n)*2^(n-1) - [n=0]. - _G. C. Greubel_, Oct 26 2022
%t A142710 Join[{2},LinearRecurrence[{2,7,-12,-11,16,-4},{2,6,14,38,112,276},30]] (* _Harvey P. Dale_, Nov 25 2013 *)
%o A142710 (Magma) [n eq 0 select 2 else (-1)^n*Lucas(n) +Lucas(2*n) -(1+(-1)^n)*2^(n-1): n in [0..50]]; // _G. C. Greubel_, Oct 26 2022
%o A142710 (SageMath)
%o A142710 def A142710(n): return (-1)^n*lucas_number2(n,1,-1) + lucas_number2(2*n,1,-1) - (1 + (-1)^n)*2^(n-1) -int(n==0)
%o A142710 [A142710(n) for n in range(51)] # _G. C. Greubel_, Oct 26 2022
%Y A142710 Cf. A000032, A014217, A142585, A142586, A147586.
%K A142710 nonn,easy
%O A142710 0,1
%A A142710 _Paul Curtz_, Sep 25 2008
%E A142710 Offset set to zero and extended - _R. J. Mathar_, Jun 14 2010