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A154964 a(n) = 3*a(n-1) + 6*a(n-2), n>2, a(0)=1, a(1)=1, a(2)=5. 9
1, 1, 5, 21, 93, 405, 1773, 7749, 33885, 148149, 647757, 2832165, 12383037, 54142101, 236724525, 1035026181, 4525425693, 19786434165, 86511856653, 378254174949, 1653833664765, 7231026043989, 31616080120557, 138234396625605, 604399670600157, 2642605391554101 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n>=1, a(n) is the number of words of length n-1 over the alphabet {1,2,3,4,5} such that no two even numbers appear consecutively. - Armend Shabani, Mar 01 2017

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (3,6).

FORMULA

G.f.: (1 - 2*x - 4*x^2)/(1 - 3*x - 6*x^2).

a(n+1) = Sum_{k=0..n} A154929(n,k)*2^(n-k).

a(n) = (1/2)*(((3/2)-(1/2)*sqrt(33))^(n-1)+((3/2)+(1/2)*sqrt(33))^(n-1))+(7/66)*sqrt(33)*(((3/2)+(1/2)*sqrt(33))^(n-1)-((3/2)-(1/2)*sqrt(33))^(n-1))+(2/3)*(C(2*n,n) mod 2). - Paolo P. Lava, Jan 20 2009

G.f.: Q(0)/6 +2/3 , where Q(k) = 1 + 1/(1 - x*(6*k+3 + 6*x )/( x*(6*k+6 + 6*x ) + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 21 2013

MATHEMATICA

{1}~Join~LinearRecurrence[{3, 6}, {1, 5}, 25] (* or *)

CoefficientList[Series[(1 - 2 x - 4 x^2)/(1 - 3 x - 6 x^2), {x, 0, 25}], x] (* Michael De Vlieger, Mar 02 2017 *)

PROG

(PARI) Vec((1-2*x-4*x^2)/(1-3*x-6*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 11 2012

CROSSREFS

Sequence in context: A168444 A125784 A218964 * A007287 A116904 A126952

Adjacent sequences:  A154961 A154962 A154963 * A154965 A154966 A154967

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Jan 18 2009

STATUS

approved

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Last modified March 19 18:49 EDT 2019. Contains 321330 sequences. (Running on oeis4.)