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Revision History for A173674
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
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COMMENTS
The 500th iteration:
Table[N[Ceiling[a[n + 1]/2]/Floor[a[n]/2]], {n, 4, 500}][[500 - 4]]
gives:
1.3802775690976141.
The x^4 - x^3 - 1 root ratio limit of A003296 is:
1.3802775690976141.
MATHEMATICA
ab[0] = 0; ab[1] = 1; ab[2] = 1; ab[3] = 1;
ab[n_] := ab[n] = ab[n - 1] + ab[n - 4]
Table[ab[n] - Floor[ab[n]/2], {n, 0, 30}]
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NAME
ceil[a(n) = ceiling(A003269(n)/2]).
COMMENTS
The x^4 - x^3 - 1 root ratio limit of A003296 is:
FORMULA
a(n) = A003269(n) -Floor[ floor(A003269(n)/2]):
a(n) =Ceiling[ ceiling(A003269(n)/2]).
a(n)= +a(n-1) + a(n-4) + a(n-15) - a(n-16) - a(n-19). - R. J. Mathar, Sep 10 2016
CROSSREFS
Cf. A003269.
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LINKS
<a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, order 19signature (1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1).
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