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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

%I

%S 1,1,5,21,93,405,1773,7749,33885,148149,647757,2832165,12383037,

%T 54142101,236724525,1035026181,4525425693,19786434165,86511856653,

%U 378254174949,1653833664765,7231026043989,31616080120557,138234396625605,604399670600157,2642605391554101

%N a(n) = 3*a(n-1) + 6*a(n-2), n>2, a(0)=1, a(1)=1, a(2)=5.

%C 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

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,6).

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

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

%F 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

%F 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

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

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

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

%K nonn,easy

%O 0,3

%A _Philippe Deléham_, Jan 18 2009

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Last modified April 19 16:58 EDT 2019. Contains 322283 sequences. (Running on oeis4.)