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 A085480 Expansion of 3*x*(1+2*x)/(1-3*x-3*x^2). 4
 0, 3, 15, 54, 207, 783, 2970, 11259, 42687, 161838, 613575, 2326239, 8819442, 33437043, 126769455, 480619494, 1822166847, 6908359023, 26191577610, 99299809899, 376474162527, 1427321917278, 5411388239415, 20516130470079 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A Jacobsthal variation. p - q = sqrt(21); p*q = -3; p + q = 3. REFERENCES Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001, p. 471. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (3,3). FORMULA a(n) = p^n + q^n, where p = (3 + sqrt(21))/2, q = (3 - sqrt 21)/2. a(n) = 3*a(n-1) + 3*a(n-2), a(1)=3, a(2)=15. - Philippe Deléham, Nov 19 2008 G.f.: G(0)/x - 2/x, where G(k) = 1 + 1/(1 - x*(7*k-3)/(x*(7*k+4) - 2/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013 EXAMPLE a(4) = q^4 + q^4 = 207; p^5 + q^5 = 783, where p = (3 + sqrt(21))/2, q = (3 - sqrt(21))/2. MATHEMATICA CoefficientList[Series[3x (1+2x)/(1-3x-3x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, 3}, {0, 3, 15}, 30] (* Harvey P. Dale, Jan 10 2021 *) CROSSREFS Cf. A030195. Sequence in context: A290764 A286986 A261565 * A265974 A099581 A026696 Adjacent sequences: A085477 A085478 A085479 * A085481 A085482 A085483 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Jul 02 2003 EXTENSIONS Zero prepended by Harvey P. Dale, Jan 10 2021 STATUS approved

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)