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 A159287 Expansion of x^2/(1-x^2-2*x^3). 7
 0, 0, 1, 0, 1, 2, 1, 4, 5, 6, 13, 16, 25, 42, 57, 92, 141, 206, 325, 488, 737, 1138, 1713, 2612, 3989, 6038, 9213, 14016, 21289, 32442, 49321, 75020, 114205, 173662, 264245, 402072, 611569, 930562, 1415713, 2153700, 3276837, 4985126, 7584237, 11538800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS A floretion-generated sequence: 'i + 0.5('ij' + 'ik' + 'ji' + 'jk' + 'ki' + 'kj'). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Creighton Dement, Online Floretion Multiplier. [broken link] Yüksel Soykan, A Study on Generalized Jacobsthal-Padovan Numbers, Earthline Journal of Mathematical Sciences (2020) Vol. 4, No. 2, 227-251. Index entries for linear recurrences with constant coefficients, signature (0,1,2). FORMULA G.f.: x^2/(1-x^2-2*x^3). a(n) = A052947(n-2). - R. J. Mathar, Nov 10 2009 a(n) = a(n-2) + 2*a(n-3). - Wesley Ivan Hurt, May 23 2023 MATHEMATICA LinearRecurrence[{0, 1, 2}, {0, 0, 1}, 60] (* Vladimir Joseph Stephan Orlovsky, May 24 2011 *) CoefficientList[Series[x^2/(1-x^2-2x^3), {x, 0, 50}], x] (* Harvey P. Dale, May 29 2021 *) PROG (PARI) a(n)=([0, 1, 0; 0, 0, 1; 2, 1, 0]^n*[0; 0; 1])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016 (Magma) I:=[0, 0, 1]; [n le 3 select I[n] else Self(n-2) + 2*Self(n-3): n in [1..30]]; // G. C. Greubel, Jun 27 2018 CROSSREFS Cf. A159284, A159285, A159286, A159288. Essentially the same as A052947. Sequence in context: A351253 A110332 A052947 * A252448 A021992 A337123 Adjacent sequences: A159284 A159285 A159286 * A159288 A159289 A159290 KEYWORD easy,nonn AUTHOR Creighton Dement, Apr 08 2009 STATUS approved

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Last modified August 8 03:17 EDT 2024. Contains 375018 sequences. (Running on oeis4.)