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A137241
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Number triples (k,3-k,2-2k), concatenated for k=0, 1, 2, 3,...
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5
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0, 3, 2, 1, 2, 0, 2, 1, -2, 3, 0, -4, 4, -1, -6, 5, -2, -8, 6, -3, -10, 7, -4, -12, 8, -5, -14, 9, -6, -16, 10, -7, -18, 11, -8, -20, 12, -9, -22, 13, -10, -24, 14, -11, -26, 15, -12, -28, 16, -13, -30, 17, -14, -32, 18, -15, -34, 19, -16, -36, 20, -17, -38, 21, -18, -40
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OFFSET
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0,2
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COMMENTS
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The entries are the coefficients in a family of Jacobsthal recurrences: a(n)=k*a(n-1)+(3-k)*a(n-2)+(2-2k)*a(n-3).
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LINKS
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FORMULA
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a(n) = 2*a(n-3) - a(n-6).
G.f.: x*(3+2*x+x^2-4*x^3-4*x^4)/((x-1)^2*(1+x+x^2)^2). (End)
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EXAMPLE
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The triples (k,3-k,2-2k) are (0,3,2), (1,2,0), (2,1,-2), (3,0,-4),...
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MATHEMATICA
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CoefficientList[Series[x*(3 + 2*x + x^2 - 4*x^3 - 4*x^4)/((x - 1)^2*(1 + x + x^2)^2), {x, 0, 50}], x] (* G. C. Greubel, Sep 28 2017 *)
Table[{n, 3-n, 2-2n}, {n, 0, 30}]//Flatten (* or *) LinearRecurrence[ {0, 0, 2, 0, 0, -1}, {0, 3, 2, 1, 2, 0}, 100] (* Harvey P. Dale, Jun 23 2019 *)
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PROG
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(PARI) x='x+O('x^50); Vec(x*(3+2*x+x^2-4*x^3-4*x^4)/((x-1)^2*(1+x +x^2 )^2)) \\ G. C. Greubel, Sep 28 2017
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CROSSREFS
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KEYWORD
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easy,sign,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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