

A099524


Expansion of 1/(15*xx^3).


0



1, 5, 25, 126, 635, 3200, 16126, 81265, 409525, 2063751, 10400020, 52409625, 264111876, 1330959400, 6707206625, 33800145001, 170331684405, 858365628650, 4325628288251, 21798473125660, 109850731256950, 553579284573001
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OFFSET

0,2


COMMENTS

A transform of A000351 under the mapping mapping g(x)>(1/(1x^3))g(x/(1x^3)).
a(n) equals the number of nlength 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

Table of n, a(n) for n=0..21.
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(n1) + a(n3).
a(n) = Sum_(k=0..floor(n/3)) binomial(n2*k, k)*5^(n3*k).


MATHEMATICA

CoefficientList[Series[1/(15xx^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



