A219088 a(n) = floor((n + 1/2)^5).

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

Offset: 0

Author

Clark Kimberling, Jan 01 2013

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A219085.

Programs

Mathematica

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

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