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 A099524 Expansion of 1/(1-5*x-x^3). 0
 1, 5, 25, 126, 635, 3200, 16126, 81265, 409525, 2063751, 10400020, 52409625, 264111876, 1330959400, 6707206625, 33800145001, 170331684405, 858365628650, 4325628288251, 21798473125660, 109850731256950, 553579284573001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A transform of A000351 under the mapping mapping g(x)->(1/(1-x^3))g(x/(1-x^3)). a(n) equals the number of n-length words on {0,1,2,3,4,5} such that 0 appears only in a run which length is a multiple of 3. - Milan Janjic, Feb 17 2015 LINKS Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3 Index entries for linear recurrences with constant coefficients, signature (5,0,1). FORMULA a(n) = 5*a(n-1) + a(n-3). a(n) = Sum_(k=0..floor(n/3)) binomial(n-2*k, k)*5^(n-3*k). MATHEMATICA CoefficientList[Series[1/(1-5x-x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[ {5, 0, 1}, {1, 5, 25}, 30] (* Harvey P. Dale, May 08 2012 *) CROSSREFS Cf. A099504. Sequence in context: A173260 A080516 A033141 * A081916 A307879 A082308 Adjacent sequences:  A099521 A099522 A099523 * A099525 A099526 A099527 KEYWORD nonn,easy AUTHOR Paul Barry, Oct 20 2004 STATUS approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)