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 A098156 #46 Mar 26 2025 19:12:28
%S A098156 1,2,5,13,32,76,176,400,896,1984,4352,9472,20480,44032,94208,200704,
%T A098156 425984,901120,1900544,3997696,8388608,17563648,36700160,76546048,
%U A098156 159383552,331350016,687865856,1426063360,2952790016,6106906624
%N A098156 Interleave n+1 and 2n+1 and take binomial transform.
%C A098156 Binomial transform of A029579.
%C A098156 An elephant sequence, see A175655. For the central square 16 A[5] vectors, with decimal values between 59 and 440, lead to this sequence (without a(1)). For the corner squares these vectors lead to the companion sequence A066373 (with a leading 1 added). - _Johannes W. Meijer_, Aug 15 2010
%H A098156 Vincenzo Librandi, <a href="/A098156/b098156.txt">Table of n, a(n) for n = 0..1000</a>
%H A098156 David Anderson, E. S. Egge, M. Riehl, L. Ryan, R. Steinke, Y. Vaughan, <a href="http://arxiv.org/abs/1605.06825">Pattern Avoiding Linear Extensions of Rectangular Posets</a>, arXiv:1605.06825 [math.CO], 2016.
%H A098156 Colin Defant, <a href="https://arxiv.org/abs/1905.02309">Proofs of Conjectures about Pattern-Avoiding Linear Extensions</a>, arXiv:1905.02309 [math.CO], 2019.
%H A098156 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F A098156 G.f.: (1-2*x+x^2+x^3)/(1-2*x)^2.
%F A098156 a(n) = (2 * 0^n + Sum_{k=0..n} (-1)^(n-k)*k*binomial(n,k) + 2^(n+1) + 3*n*2^(n-1) )/4.
%F A098156 a(n) = Sum_{j=0..n} Sum_{k=0..n} binomial(n, 2*(k-j)).
%F A098156 a(n) = Sum_{k=0..n} Sum_{j=0..k} C(n, 2*j). - _Paul Barry_, Jan 13 2005
%F A098156 a(n) = 2^(n-3)*(3*n+4) for n>=2. - _Philip B. Zhang_, May 25 2016
%F A098156 E.g.f.: (2 + x + (2 + 3*x)*exp(2*x))/4. - _Ilya Gutkovskiy_, May 31 2016
%t A098156 CoefficientList[Series[(1-2x+x^2+x^3)/(1-2x)^2, {x, 0, 40}], x] (* _Vincenzo Librandi_, Jul 21 2013 *)
%t A098156 LinearRecurrence[{4,-4},{1,2,5,13},50] (* _Harvey P. Dale_, Dec 03 2023 *)
%o A098156 (PARI) {a(n) = if(n==0,1, if(n==1,2, 2^(n-3)*(3*n+4)))}; \\ _G. C. Greubel_, May 08 2019
%o A098156 (Magma) [1,2] cat [2^(n-3)*(3*n+4): n in [2..40]]; // _G. C. Greubel_, May 08 2019
%o A098156 (Sage) [1,2]+[2^(n-3)*(3*n+4) for n in (2..40)] # _G. C. Greubel_, May 08 2019
%o A098156 (GAP) Concatenation([1,2], List([2..40], n-> 2^(n-3)*(3*n+4))); # _G. C. Greubel_, May 08 2019
%K A098156 easy,nonn
%O A098156 0,2
%A A098156 _Paul Barry_, Aug 29 2004