A034131 - OEIS

%I #28 May 04 2026 18:24:00

%S 4,16,43,92,167,275,422,615,858,1158,1521,1954,2461,3049,3724,4493,

%T 5360,6332,7415,8616,9939,11391,12978,14707,16582,18610,20797,23150,

%U 25673,28373,31256,34329,37596,41064,44739,48628,52735,57067,61630,66431,71474,76766,82313

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

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

%H Zhuorui He, <a href="/A034131/b034131.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1,-3,3,-1).

%F a(n) = ceiling((n + 1/2)^3). - _Benoit Cloitre_, Apr 16 2003

%F 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

%F a(n) = A219085(n) + 1. - _Zhuorui He_, Dec 05 2025

%F 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

%t Ceiling[(Range[50] + 1/2)^3] (* _Paolo Xausa_, May 04 2026 *)

%Y Cf. A034121, A219085.

%K nonn,easy

%O 1,1

%A _Patrick De Geest_, Sep 15 1998

%E New name from formula by _Zhuorui He_, Dec 05 2025