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 A138395 a(n) = 6*a(n-1) - 3*a(n-2), a(1) = 1, a(2) = 6. 10
 1, 6, 33, 180, 981, 5346, 29133, 158760, 865161, 4714686, 25692633, 140011740, 762992541, 4157920026, 22658542533, 123477495120, 672889343121, 3666903573366, 19982753410833, 108895809744900, 593426598236901, 3233872160186706, 17622953166409533 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) equals the number of words of length n-1 over {0,1,2,3,4,5} avoiding 01, 02 and 03. - Milan Janjic, Dec 17 2015 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (6,-3). FORMULA Limit_{n->oo} a(n)/a(n-1) = 3 + sqrt(6) = 5.44948974... a(n) = ((3+sqrt(6))^n - (3-sqrt(6))^n)/(2*sqrt(6)). - Alexander R. Povolotsky, Apr 01 2008 a(n) = lower left term of n-th power of 2 X 2 matrix [1,2; 1,5]. G.f.: 1/(1 - 6*x + 3*x^2). - Philippe Deléham, Sep 09 2009 a(n) = Chebyshev_U(n, sqrt(3))*(sqrt(3))^n. - Paul Barry, Sep 28 2009 EXAMPLE a(5) = 981 = 6*a(4) - 3*a(3) = 6*180 - 3*33. MATHEMATICA a[n_]:=(MatrixPower[{{1, 2}, {1, 5}}, n].{{1}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *) LinearRecurrence[{6, -3}, {1, 6}, 30] (* Harvey P. Dale, Jan 18 2012 *) PROG (Magma) I:=[1, 6]; [n le 2 select I[n] else 6*Self(n-1)-3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Dec 17 2015 (PARI) Vec(1/(1-6*x+3*x^2) + O(x^100)) \\ Altug Alkan, Dec 17 2015 (SageMath) A138395=BinaryRecurrenceSequence(6, -3, 0, 1) [A138395(n) for n in range(1, 30)] # G. C. Greubel, Jan 10 2024 CROSSREFS Cf. A084120, A190958. Sequence in context: A111994 A092851 A137627 * A050151 A009162 A012718 Adjacent sequences: A138392 A138393 A138394 * A138396 A138397 A138398 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Mar 19 2008 EXTENSIONS More terms from Philippe Deléham, Sep 09 2009 a(21) and first formula corrected by Klaus Brockhaus, Oct 05 2009 Extended by T. D. Noe, May 23 2011 STATUS approved

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Last modified August 11 20:46 EDT 2024. Contains 375073 sequences. (Running on oeis4.)