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3, 12, 42, 123, 366, 1092, 3279, 9840, 29526, 88575, 265722, 797160, 2391483, 7174452, 21523362, 64570083, 193710246, 581130732, 1743392199, 5230176600, 15690529806, 47071589415, 141214768242, 423644304720, 1270932914163
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OFFSET
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0,1
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COMMENTS
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Digital roots yield a hexaperiodic sequence A010888(a(n))= 3*A135265(n+1).
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4).
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MAPLE
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seq(coeff(series(3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4), x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 21 2019
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MATHEMATICA
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LinearRecurrence[{3, 0, -1, 3}, {3, 12, 42, 123}, 25] (* G. C. Greubel, Oct 07 2016 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec(3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4)) \\ G. C. Greubel, Nov 21 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4) )); // G. C. Greubel, Nov 21 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P(3*(1+x+2*x^2)/(1-3*x+x^3-3*x^4)).list()
(GAP) a:=[3, 12, 42, 123];; for n in [5..30] do a[n]:=3*a[n-1]-a[n-3]+ 3*a[n-4]; od; a; # G. C. Greubel, Nov 21 2019
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CROSSREFS
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KEYWORD
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nonn,less,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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