A010014 a(0) = 1, a(n) = 24*n^2 + 2 for n>0.

1, 26, 98, 218, 386, 602, 866, 1178, 1538, 1946, 2402, 2906, 3458, 4058, 4706, 5402, 6146, 6938, 7778, 8666, 9602, 10586, 11618, 12698, 13826, 15002, 16226, 17498, 18818, 20186, 21602, 23066, 24578, 26138, 27746, 29402, 31106, 32858, 34658, 36506, 38402, 40346

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of points of L_infinity norm n in the simple cubic lattice Z^3. - N. J. A. Sloane, Apr 15 2008

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

First bisection of A005897. After 1, all terms are in A000408. - Bruno Berselli, Feb 06 2012

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Xavier Acloque, Polynexus Numbers and other mathematical wonders [broken link]
• Victor Kamel, Hanxueyu Yan, and Sean Chester, CLOVER: A GPU-native, Spatio-graph-based Approach to Exact kNN, ACM Int'l Conf. Supercomp. (ICS 2025). See p. 3.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A206399.

Programs

Mathematica

Join[{1}, 24 Range[41]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)

PARI

a(n) = if (n==0, 1, 24*n^2 + 2);
vector(40, n, a(n-1)) \\ Altug Alkan, Sep 29 2015

Formula

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

G.f.: (1+x)*(1+22*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012

a(n) = (2*n-1)^2 + (2*n+1)^2 + (4*n)^2 for n>0. - Bruno Berselli, Feb 06 2012

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

a(n) = A005899(n) + A195322(n), n > 0. - R. J. Cano, Sep 29 2015

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

a(n) = 2*A158480(n), n>0. - R. J. Mathar, May 07 2024

a(n) = A069190(n)+A069190(n+1). - R. J. Mathar, May 07 2024

Extensions

More terms from Xavier Acloque, Oct 20 2003