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 A098156 Interleave n+1 and 2n+1 and take binomial transform. 5
 1, 2, 5, 13, 32, 76, 176, 400, 896, 1984, 4352, 9472, 20480, 44032, 94208, 200704, 425984, 901120, 1900544, 3997696, 8388608, 17563648, 36700160, 76546048, 159383552, 331350016, 687865856, 1426063360, 2952790016, 6106906624 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A029579. 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] LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 David Anderson, E. S. Egge, M. Riehl, L. Ryan, R. Steinke, Y. Vaughan, Pattern Avoiding Linear Extensions of Rectangular Posets, arXiv preprint arXiv:1605.06825 [math.CO], 2016. Index entries for linear recurrences with constant coefficients, signature (4,-4). FORMULA G.f.: (1-2*x+x^2+x^3)/(1-2*x)^2. a(n) = 0^n/2+sum{k=0..n, binomial(-1)^(n-k)*k)}/4+2^n/2+3n*2^(n-1)/4. a(n) = sum{j=0..n, sum{k=0..n, binomial(n, 2(k-j)}}. a(n) = sum{k=0..n, sum{i=0..k, C(n, 2i)}}. - Paul Barry, Jan 13 2005 a(n) = 2^(n-3)*(3*n+4) for n>=2. - Philip B. Zhang, May 25 2016 E.g.f.: (2 + x + (2 + 3*x)*exp(2*x))/4. - Ilya Gutkovskiy, May 31 2016 MATHEMATICA CoefficientList[Series[(1 - 2 x + x^2 + x^3) / (1 - 2 x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 21 2013 *) CROSSREFS Sequence in context: A086758 A179257 A116702 * A267862 A098586 A199812 Adjacent sequences:  A098153 A098154 A098155 * A098157 A098158 A098159 KEYWORD easy,nonn AUTHOR Paul Barry, Aug 29 2004 STATUS approved

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Last modified October 22 11:11 EDT 2018. Contains 316438 sequences. (Running on oeis4.)