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 A055989 a(n) is its own 4th difference. 4
 1, 3, 10, 36, 131, 476, 1728, 6272, 22765, 82629, 299915, 1088589, 3951206, 14341527, 52054840, 188941273, 685792227, 2489191330, 9034913540, 32793647355, 119029728628, 432037221840, 1568147413312, 5691839002677 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (5,-6,4,-1). FORMULA a(n) = 5*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) = a(n-1) + A055988(n) = A055990(n) - A055990(n-1) = A055991(n) - 2*A055991(n-1) + A055991(n-2). G.f.: x*(1-x)^2/(1 - 5*x + 6*x^2 - 4*x^3 + x^4). - Colin Barker Apr 04 2012 MATHEMATICA CoefficientList[Series[(1-x)^2/(1-5*x+6*x^2-4*x^3+x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 05 2012 *) LinearRecurrence[{5, -6, 4, -1}, {1, 3, 10, 36}, 30] (* Harvey P. Dale, Jan 10 2014 *) PROG (Magma) I:=[1, 3, 10, 36]; [n le 4 select I[n] else 5*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Apr 05 2012 CROSSREFS Cf. A055988, A055990, A055991 for the other differences of a(n). See A000079, A001906, A052529 for examples of sequences which are respectively their own first, second and third differences. Sequence in context: A047122 A047107 A149040 * A329533 A102871 A277287 Adjacent sequences: A055986 A055987 A055988 * A055990 A055991 A055992 KEYWORD nonn,easy AUTHOR Henry Bottomley, Jun 02 2000 EXTENSIONS More terms from James A. Sellers, Jun 05 2000 STATUS approved

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Last modified December 8 07:08 EST 2022. Contains 358673 sequences. (Running on oeis4.)