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 A134396 A007318 * A000125. 3
 1, 3, 9, 27, 80, 232, 656, 1808, 4864, 12800, 33024, 83712, 208896, 514048, 1249280, 3002368, 7143424, 16842752, 39387136, 91422720, 210763776, 482869248, 1099956224, 2492465152, 5620367360, 12616466432, 28202500096, 62797119488, 139318001664, 308029685760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is the number of ternary strings of length n that contain at most three 0's.- Enrique Navarrete, Mar 13 2024 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16). FORMULA Binomial transform of A000125. Row sums of triangle A134395. O.g.f.: (1-x)*(1-4*x+5*x^2) / (1-2*x)^4. - R. J. Mathar, Jun 08 2008 From Colin Barker, Feb 13 2017: (Start) a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n>3. a(n) = (2^(n-4)*(48 + 20*n + 3*n^2 + n^3)) / 3. (End) E.g.f.: e^(2*x)*(1+x+x^2/2+x^3/6). - Enrique Navarrete, Mar 13 2024 EXAMPLE a(3) = 27 = (1, 3, 3, 1) dot (1, 2, 4, 8) = (1 + 6 + 12 + 8), where A000125 = (1, 2, 4, 8, 15, 26, 42, ...). a(3) = 27 = sum of row 3 terms of triangle A134395: (8 + 12 + 6 + 1). MATHEMATICA CoefficientList[Series[(1-x)(1-4x+5x^2)/(1-2x)^4, {x, 0, 30}], x] (* or *) LinearRecurrence[ {8, -24, 32, -16}, {1, 3, 9, 27}, 30] (* Harvey P. Dale, Mar 09 2023 *) PROG (PARI) Vec((1-x)*(1-4*x+5*x^2) / (1-2*x)^4 + O(x^30)) \\ Colin Barker, Feb 13 2017 CROSSREFS Cf. A134395, A000125. Sequence in context: A304067 A287898 A129770 * A059502 A291006 A289781 Adjacent sequences: A134393 A134394 A134395 * A134397 A134398 A134399 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Oct 23 2007 EXTENSIONS More terms from R. J. Mathar, Jun 08 2008 STATUS approved

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Last modified September 14 12:31 EDT 2024. Contains 375921 sequences. (Running on oeis4.)