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A065692
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Braided power sequence: this is b(n+1)=3b(n)+2d(n)-c(n), A065693 is c(n+1)=3c(n)+2b(n)-d(n) and A065694 is d(n+1)=3d(n)+2c(n)-b(n), starting with b(0)=0, c(0)=1 and d(0)=2.
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2
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0, 3, 24, 117, 417, 1140, 2583, 7311, 39840, 251613, 1329969, 5738172, 20838447, 67344735, 216818808, 812592261, 3660235905, 17401156548, 78077421639, 318790895727, 1197423287952, 4316735957805, 15912781695633
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OFFSET
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0,2
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COMMENTS
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Tends to 4^n. "Braided" because the order of b(n), c(n) and d(n) changes between the six possibilities as n increases.
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LINKS
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FORMULA
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a(n) = 9*a(n-1)-33*a(n-2)+52*a(n-3) for n>2.
G.f.: 3*x*(1-x) / ((1-4*x)*(1-5*x+13*x^2)).
(End)
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EXAMPLE
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a(1) = 3*0+2*2-1*1 = 3.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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