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 A120656 a(n) = (-4 + (-2)^n + 2*3^(n+1))/3 - [n=0]. 1
 0, 4, 18, 50, 166, 474, 1478, 4330, 13206, 39194, 118438, 353610, 1064246, 3185914, 9571398, 28686890, 86115286, 258236634, 774928358, 2324348170, 6973918326, 20920007354, 62763517318, 188283561450, 564864665366, 1694566034074 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,5,-6). FORMULA From Colin Barker, Oct 19 2012: (Start) a(n) = (-4 + (-2)^n + 2*3^(n+1))/3 - [n=0]. a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3) for n>3. G.f.: 2*x*(2-x)*(1+3*x)/((1-x)*(1+2*x)*(1-3*x)). (End) E.g.f.: (1/3)*(exp(-2*x) - 3 - 4*exp(x) + 6*exp(3*x)). - G. C. Greubel, Dec 25 2022 MATHEMATICA LinearRecurrence[{2, 5, -6}, {0, 4, 18, 50}, 51] (* Harvey P. Dale, Oct 18 2014 *) PROG (Magma) [0] cat [(-4 + (-2)^n + 2*3^(n+1))/3: n in [1..50]]; // G. C. Greubel, Dec 25 2022 (SageMath) [(-4 + (-2)^n + 2*3^(n+1))/3 -int(n==0) for n in range(51)] # G. C. Greubel, Dec 25 2022 CROSSREFS Cf. A120655. Sequence in context: A353162 A303737 A180805 * A256431 A256430 A225263 Adjacent sequences: A120653 A120654 A120655 * A120657 A120658 A120659 KEYWORD nonn,less AUTHOR Roger L. Bagula, Aug 10 2006 EXTENSIONS Edited by G. C. Greubel, Dec 25 2022 Meaningful name using given formula from Joerg Arndt, Dec 26 2022 STATUS approved

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Last modified August 9 20:51 EDT 2024. Contains 375044 sequences. (Running on oeis4.)