A034131 a(n) = ceiling((n + 1/2)^3).

4, 16, 43, 92, 167, 275, 422, 615, 858, 1158, 1521, 1954, 2461, 3049, 3724, 4493, 5360, 6332, 7415, 8616, 9939, 11391, 12978, 14707, 16582, 18610, 20797, 23150, 25673, 28373, 31256, 34329, 37596, 41064, 44739, 48628, 52735, 57067, 61630, 66431, 71474, 76766, 82313

Offset

1,1

Comments

Previous name was: Decimal part of cube root of a(n) starts with 5: first term of runs.

Links

Zhuorui He, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1,-3,3,-1).

Formula

a(n) = ceiling((n + 1/2)^3). - Benoit Cloitre, Apr 16 2003

a(n) = (1/8)*(8*n^3 + 12*n^2 + 6*n + 5 + (-1)^n + 2*(-1)^floor(n/2)). - Ralf Stephan, Jun 10 2005

a(n) = A219085(n) + 1. - Zhuorui He, Dec 05 2025

G.f.: x*(4 + 4*x + 7*x^2 + 7*x^3 + 3*x^5 - x^6)/((1 - x)^4*(1 + x + x^2 + x^3)). - Stefano Spezia, Dec 08 2025

Mathematica

Ceiling[(Range[50] + 1/2)^3] (* Paolo Xausa, May 04 2026 *)

Crossrefs

Cf. A034121, A219085.

Sequence in context: A344857 A190090 A227012 * A183536 A320100 A161142

Adjacent sequences: A034128 A034129 A034130 * A034132 A034133 A034134

Keyword

nonn,easy

Author

Patrick De Geest, Sep 15 1998

Extensions

New name from formula by Zhuorui He, Dec 05 2025

Status

approved