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A228842
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Binomial transform of A014448.
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3
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2, 6, 28, 144, 752, 3936, 20608, 107904, 564992, 2958336, 15490048, 81106944, 424681472, 2223661056, 11643240448, 60964798464, 319215828992, 1671435780096, 8751751364608, 45824765067264, 239941584945152, 1256350449401856, 6578336356630528, 34444616342175744
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OFFSET
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0,1
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COMMENTS
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The binomial transform of this sequence is 2, 8, 42, 248,... = 2*A108404(n).
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REFERENCES
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C. Smith, A Treatise on Algebra, Macmillan, London, 5th ed., 1950, p. 360, Example 44.
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LINKS
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FORMULA
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G.f.: 2*( 1-3*x ) / ( 1-6*x+4*x^2 ).
a(n) = (3-sqrt(5))^n + (3+sqrt(5))^n.
a(n) = 6*a(n-1) - 4*a(n-2) for n>1.
(End)
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MATHEMATICA
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CoefficientList[Series[2*(1 - 3 x)/(1 - 6 x + 4 x^2), {x, 0, 23}], x] (* Michael De Vlieger, Aug 26 2021 *)
LinearRecurrence[{6, -4}, {2, 6}, 30] (* Harvey P. Dale, Jun 30 2024 *)
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PROG
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(PARI) Vec(2*(1 - 3*x) / (1 - 6*x + 4*x^2) + O(x^30)) \\ Colin Barker, Sep 21 2017
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CROSSREFS
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When divided by 2^n this becomes(essentially) A005248.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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