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A219088 Floor((n + 1/2)^5). 2
0, 7, 97, 525, 1845, 5032, 11602, 23730, 44370, 77378, 127628, 201135, 305175, 448403, 640973, 894660, 1222981, 1641308, 2166998, 2819506, 3620506, 4594013, 5766503, 7167031, 8827351, 10782039, 13068609, 15727636, 18802876 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

LINKS

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).

FORMULA

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

MATHEMATICA

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

CROSSREFS

Cf. A219085.

Sequence in context: A116125 A142315 A116288 * A116261 A289851 A242377

Adjacent sequences:  A219085 A219086 A219087 * A219089 A219090 A219091

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jan 01 2013

STATUS

approved

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Last modified August 17 15:35 EDT 2022. Contains 356189 sequences. (Running on oeis4.)