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A184635
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a(n) = floor(1/{(n+n^4)^(1/4)}), where {} = fractional part.
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1
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5, 16, 36, 64, 100, 144, 196, 256, 324, 400, 484, 576, 676, 784, 900, 1024, 1156, 1296, 1444, 1600, 1764, 1936, 2116, 2304, 2500, 2704, 2916, 3136, 3364, 3600, 3844, 4096, 4356, 4624, 4900, 5184, 5476, 5776, 6084, 6400, 6724, 7056, 7396, 7744, 8100, 8464
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..46.
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
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FORMULA
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a(n) = floor(1/{(n+n^4)^(1/4)}), where {} = fractional part.
It appears that a(n)=3a(n-1)-3a(n-2)+a(n-3) for n>=5, and that a(n)=4*n^2 for n>=2.
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MATHEMATICA
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p[n_]:=FractionalPart[(n^4+n)^(1/4)];
q[n_]:=Floor[1/p[n]];
Table[q[n], {n, 1, 80}]
FindLinearRecurrence[Table[q[n], {n, 1, 1000}]]
Join[{5}, LinearRecurrence[{3, -3, 1}, {16, 36, 64}, 45]] (* Ray Chandler, Aug 02 2015 *)
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CROSSREFS
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Cf. A184536, A144916, A016742.
Sequence in context: A234362 A108966 A321019 * A328506 A072333 A055232
Adjacent sequences: A184632 A184633 A184634 * A184636 A184637 A184638
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Jan 18 2011
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STATUS
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approved
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