A046949 Sizes of successive balls in D_4 lattice.

1, 25, 49, 145, 169, 313, 409, 601, 625, 937, 1081, 1369, 1465, 1801, 1993, 2569, 2593, 3025, 3337, 3817, 3961, 4729, 5017, 5593, 5689, 6433, 6769, 7729, 7921, 8641, 9217, 9985, 10009, 11161, 11593, 12745, 13057, 13969, 14449, 15793

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

The subsequence of primes in this partial sum begins: 313, 409, 601, 937, 1801, 1993, 2593, 4729, 5689, 8641, 10009, 11161, 11593, 14449. [Jonathan Vos Post, Feb 18 2010]

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to D_4 lattice

Crossrefs

Partial sums of A004011.

Programs

Mathematica

A004011 = Join[{1}, Table[24*Sum[d*Mod[d, 2], {d, Divisors[n]}], {n, 1, 40}]]; Accumulate[A004011](* Jean-François Alcover, Apr 25 2012 *)

PARI

B=1; bl=[ 1 ]; for (n=1,200,t1=divisors(2*n); t2=0; for (i=1, length(t1), if( t1[ i ]%4 <> 0, t2=t2+t1[ i ])); B=B+8*t2; bl=concat(bl,B)); bl

Formula

a(n) ~ Pi^2 * n^2. - Vaclav Kotesovec, Jan 14 2024