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A219088 Floor((n + 1/2)^5). 2

%I

%S 0,7,97,525,1845,5032,11602,23730,44370,77378,127628,201135,305175,

%T 448403,640973,894660,1222981,1641308,2166998,2819506,3620506,4594013,

%U 5766503,7167031,8827351,10782039,13068609,15727636,18802876

%N Floor((n + 1/2)^5).

%C a(n) is the number k such that {k^p} < 1/2 < {(k+1)^p}, where p = 1/5 and { } = fractional part. Equivalently, the jump sequence of f(x) = x^(1/5), in the sense that these are the nonnegative integers k for which round(k^p) < round((k+1)^p). For details and a guide to related sequences, see A219085.

%H Clark Kimberling, <a href="/A219088/b219088.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1,0,0,0,0,0,0,0,0,0,0,1,-5,10,-10,5,-1).

%F a(n) = [(n + 1/2)^5].

%F G.f.: x*(x^19 +3*x^18 +68*x^17 +106*x^16 +121*x^15 +122*x^14 +120*x^13 +118*x^12 +120*x^11 +123*x^10 +116*x^9 +123*x^8 +120*x^7 +118*x^6 +120*x^5 +122*x^4 +120*x^3 +110*x^2 +62*x +7) / ((x -1)^6*(x +1)*(x^2 +1)*(x^4 +1)*(x^8 +1)). - _Colin Barker_, Jan 06 2013

%t Table[Floor[(n + 1/2)^5], {n, 0, 100}]

%Y Cf. A219085.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jan 01 2013

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Last modified October 6 15:48 EDT 2022. Contains 357269 sequences. (Running on oeis4.)