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A065694 Braided power sequence: A065692 is b(n+1)=3b(n)+2d(n)-c(n), A065693 is c(n+1)=3c(n)+2b(n)-d(n) and this is d(n+1)=3d(n)+2c(n)-b(n), starting with b(0)=0, c(0)=1 and d(0)=2. 2

%I

%S 2,8,23,47,80,365,3089,19916,96287,369983,1188008,3489557,11440865,

%T 49588820,250207799,1210364111,5215038272,20004134333,70879879793,

%U 248964475292,941859229775,3946659132575,17384730325784,75199501505381

%N Braided power sequence: A065692 is b(n+1)=3b(n)+2d(n)-c(n), A065693 is c(n+1)=3c(n)+2b(n)-d(n) and this is d(n+1)=3d(n)+2c(n)-b(n), starting with b(0)=0, c(0)=1 and d(0)=2.

%C Tends to 4^n. "Braided" because the order of b(n), c(n) and d(n) changes between the six possibilities as n increases.

%F Conjectures from _Colin Barker_, Sep 02 2016: (Start)

%F a(n) = 9*a(n-1)-33*a(n-2)+52*a(n-3) for n>2.

%F G.f.: (2-10*x+17*x^2) / ((1-4*x)*(1-5*x+13*x^2)).

%F (End)

%e a(1) = 3*2+2*1-1*0 = 8.

%Y Cf. A065692, A065693.

%K nonn

%O 0,1

%A _Henry Bottomley_, Nov 14 2001

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Last modified May 17 08:05 EDT 2022. Contains 353741 sequences. (Running on oeis4.)