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 A116404 Expansion of (1-x)/((1-x)^2 - x^2(1+x)^2). 4
 1, 1, 2, 6, 15, 35, 84, 204, 493, 1189, 2870, 6930, 16731, 40391, 97512, 235416, 568345, 1372105, 3312554, 7997214, 19306983, 46611179, 112529340, 271669860, 655869061, 1583407981, 3822685022, 9228778026, 22280241075, 53789260175 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Diagonal sums of number triangle A114123. Binomial transform of A114122. Congruent to 1,1,0,0,1,1,... modulo 2. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Vincent Vatter, Growth rates of permutation classes: from countable to uncountable, arXiv:1605.04297 [math.CO], 2016. Index entries for linear recurrences with constant coefficients, signature (2,0,2,1). FORMULA G.f.: (1-x)/(1 - 2*x - 2*x^3 - x^4). a(n) = 2*a(n-1) + 2*a(n-3) + a(n-4). a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-k} C(2k,n-2k-j)*C(n-2k,j)*2^(n-2k-j). 2*a(n) = A056594(n) + A000129(n+1). - R. J. Mathar, Oct 25 2011 MATHEMATICA LinearRecurrence[{2, 0, 2, 1}, {1, 1, 2, 6}, 30] (* Emanuele Munarini, Apr 27 2017 *) CoefficientList[Series[(1 - x) / ((1 - x)^2 - x^2 (1 + x)^2), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 19 2017 *) PROG (PARI) Vec((1-x)/((1-x)^2-x^2*(1+x)^2) + O(x^40)) \\ Michel Marcus, Aug 19 2017 (MAGMA) I:=[1, 1, 2, 6]; [n le 4 select I[n] else 2*Self(n-1)+2*Self(n-3)+Self(n-4): n in [1..30]]; // Vincenzo Librandi, Aug 19 2017 CROSSREFS Cf. A000129, A056594, A114122, A114123. Sequence in context: A090982 A153517 A136302 * A301600 A084860 A084798 Adjacent sequences:  A116401 A116402 A116403 * A116405 A116406 A116407 KEYWORD easy,nonn AUTHOR Paul Barry, Feb 07 2006 STATUS approved

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Last modified January 22 23:00 EST 2019. Contains 319365 sequences. (Running on oeis4.)