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 A203573 Bisection of A099924 (convolution of Lucas numbers); even arguments. 3
 4, 13, 45, 152, 491, 1531, 4652, 13865, 40713, 118144, 339559, 968183, 2742100, 7721797, 21637221, 60367976, 167787107, 464776435, 1283571068, 3535240289, 9713031489, 26627195728, 72847698655, 198929987567, 542305383076, 1476061431421 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS One half of the odd part of the bisection of A099924 is found in A203574. LINKS Table of n, a(n) for n=0..25. É. Czabarka, R. Flórez, L. Junes, A Discrete Convolution on the Generalized Hosoya Triangle, Journal of Integer Sequences, 18 (2015), #15.1.6. Index entries for linear recurrences with constant coefficients, signature (6, -11, 6, -1). FORMULA a(n) = A099924(2*n), n>=0. O.g.f.: (4-11*x+11*x^2+x^3)/(1-3*x+x^2)^2. a(n) = 4*(n+1)*F(2*n+1)-(2*n+1)*F(2*n), n>=0, with the Fibonacci numbers F(n)=A000045(n). From the partial fraction decomposition of the o.g.f. and the Fibonacci recurrence. a(0)=4, a(1)=13, a(2)=45, a(3)=152, a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3)-a(n-4). - Harvey P. Dale, Jan 11 2014 MATHEMATICA CoefficientList[Series[(4-11x+11x^2+x^3)/(1-3x+x^2)^2, {x, 0, 30}], x] (* or *) LinearRecurrence[{6, -11, 6, -1}, {4, 13, 45, 152}, 30] (* Harvey P. Dale, Jan 11 2014 *) CROSSREFS Cf. A000032, A000045, A099924, 2*A203574. Sequence in context: A192255 A035356 A320652 * A214997 A189348 A165205 Adjacent sequences: A203570 A203571 A203572 * A203574 A203575 A203576 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Jan 03 2012 STATUS approved

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Last modified September 22 18:10 EDT 2023. Contains 365531 sequences. (Running on oeis4.)