0,2

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.

Clark Kimberling, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1,0,0,0,0,0,0,0,0,0,0,1,-5,10,-10,5,-1).

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

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

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

Cf. A219085.

Sequence in context: A142315 A359637 A116288 * A116261 A289851 A362472

Adjacent sequences: A219085 A219086 A219087 * A219089 A219090 A219091

nonn,easy

Clark Kimberling, Jan 01 2013

approved