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 A111961 Expansion of 1/(sqrt(1-2x-3x^2)-x). 4
 1, 2, 6, 18, 56, 176, 558, 1778, 5686, 18230, 58558, 188366, 606588, 1955044, 6305418, 20347342, 65689088, 212146400, 685342218, 2214556478, 7157409064, 23136645472, 74801223162, 241863933094, 782131232390, 2529458676326 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums of A111960. A transform of the Fibonacci numbers. - Paul Barry, Sep 23 2005 Apparently the Motzkin transform of (0 followed by A128588). - R. J. Mathar, Dec 11 2008 Inverse binomial transform of A026671. - Philippe Deléham, Feb 11 2009 Hankel transform is 2^n. - Paul Barry, Mar 02 2010 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Paul Barry, On a transformation of Riordan moment sequences, arXiv:1802.03443 [math.CO], 2018. FORMULA a(n) = Sum_{k=0..n} Sum_{j=0..n} C(n, j)*C((j-1)/2, (j-k)/2)*2^(j-k)*(1+(-1)^(j-k))/2. a(n) = Sum_{k=0..n} F(k+1)*Sum_{i=0..floor((n-k)/2)} C(n, i)*C(n-i, i+k)/(i+k+1). - Paul Barry, Sep 23 2005 G.f.: M(x)^2/(2*M(x)-M(x)^2), where M(x) is the g.f. of the Motzkin numbers A001006. - Paul Barry, Feb 03 2006 G.f.: 1/(1-2x/(1-x/(1-x^2/(1-x/(1-x/91-x^2/(1-x/(1-x/(1-x^2/(1-... (continued fraction). - Paul Barry, Mar 02 2010 D-finite with recurrence: n*a(n) + (-4*n+3)*a(n-1) + 3*(-n+1)*a(n-2) + 2*(7*n-15)*a(n-3) + 12*(n-3)*a(n-4) = 0. - R. J. Mathar, Nov 15 2012 a(n) ~ (1+sqrt(5))^n / sqrt(5). - Vaclav Kotesovec, Feb 08 2014 MATHEMATICA CoefficientList[Series[1/(Sqrt[1-2*x-3*x^2]-x), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 08 2014 *) CROSSREFS Cf. A001006, A026671, A111960, A128588. Sequence in context: A291228 A091142 A275857 * A190861 A071721 A125306 Adjacent sequences:  A111958 A111959 A111960 * A111962 A111963 A111964 KEYWORD easy,nonn AUTHOR Paul Barry, Aug 23 2005 STATUS approved

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Last modified August 3 07:58 EDT 2021. Contains 346435 sequences. (Running on oeis4.)