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 A055988 Sequence is its own 4th difference. 6
 1, 2, 7, 26, 95, 345, 1252, 4544, 16493, 59864, 217286, 788674, 2862617, 10390321, 37713313, 136886433, 496850954, 1803399103, 6545722210, 23758733815, 86236081273, 313007493212, 1136110191472, 4123691589365, 14967590689568 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums of Riordan array (1/(1-x), x/(1-x)^4), A109960. - Paul Barry, Jul 06 2005 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) = 5a(n-1) - 6a(n-2) + 4a(n-3) - a(n-4) = a(n-1) + A055991(n-1) = A055989(n) - A055989(n-1) = A055990(n) - 2*A055990(n-1) + A055990(n-2). From Paul Barry, Jul 06 2005: (Start) G.f.: (1-x)^3/(1 - 5x + 6x^2 - 4x^3 + x^4); a(n) = Sum_{k=0..n} binomial(n+3k, 4k). (End) MATHEMATICA CoefficientList[Series[(1-x)^3/(1-5x+6x^2-4x^3+x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 05 2012 *) LinearRecurrence[{5, -6, 4, -1}, {1, 2, 7, 26}, 30] (* Harvey P. Dale, Jan 15 2017 *) PROG (MAGMA) I:=[1, 2, 7, 26]; [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. A055989, 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: A289449 A188860 A129273 * A275013 A278351 A001075 Adjacent sequences:  A055985 A055986 A055987 * A055989 A055990 A055991 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 October 22 12:22 EDT 2018. Contains 316446 sequences. (Running on oeis4.)