A010014 - OEIS

%I #51 May 07 2024 06:02:58

%S 1,26,98,218,386,602,866,1178,1538,1946,2402,2906,3458,4058,4706,5402,

%T 6146,6938,7778,8666,9602,10586,11618,12698,13826,15002,16226,17498,

%U 18818,20186,21602,23066,24578,26138,27746,29402,31106,32858,34658,36506,38402,40346

%N a(0) = 1, a(n) = 24*n^2 + 2 for n>0.

%C Number of points of L_infinity norm n in the simple cubic lattice Z^3. - _N. J. A. Sloane_, Apr 15 2008

%C Numbers of cubes needed to completely "cover" another cube. - Xavier Acloque, Oct 20 2003

%C First bisection of A005897. After 1, all terms are in A000408. - _Bruno Berselli_, Feb 06 2012

%H Bruno Berselli, <a href="/A010014/b010014.txt">Table of n, a(n) for n = 0..1000</a>

%H X. Acloque <a href="http://www.fortunecity.fr/polynexus/index.html">Polynexus Numbers and other mathematical wonders</a> [broken link]

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = (2*n+1)^3 - (2*n-1)^3 for n >= 1. - Xavier Acloque, Oct 20 2003

%F G.f.: (1+x)*(1+22*x+x^2)/(1-x)^3. - _Bruno Berselli_, Feb 06 2012

%F a(n) = (2*n-1)^2 + (2*n+1)^2 + (4*n)^2 for n>0. - _Bruno Berselli_, Feb 06 2012

%F E.g.f.: (x*(x+1)*24+2)*exp(x)-1. - _Gopinath A. R._, Feb 14 2012

%F a(n) = A005899(n) + A195322(n), n > 0. - _R. J. Cano_, Sep 29 2015

%F Sum_{n>=0} 1/a(n) = 3/4 + sqrt(3)/24*Pi*coth(Pi*sqrt(3)/6) = 1.065052868574... - _R. J. Mathar_, May 07 2024

%F a(n) = 2*A158480(n), n>0. - _R. J. Mathar_, May 07 2024

%F a(n) = A069190(n)+A069190(n+1). - _R. J. Mathar_, May 07 2024

%t Join[{1}, 24 Range[41]^2 + 2] (* _Bruno Berselli_, Feb 06 2012 *)

%o (PARI) a(n) = if (n==0, 1, 24*n^2 + 2);

%o vector(40, n, a(n-1)) \\ _Altug Alkan_, Sep 29 2015

%Y Cf. A206399.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from Xavier Acloque, Oct 20 2003