A341711 a(n) = A120963(2*n+1)/2.

1, 5, 19, 59, 165, 419, 1001, 2257, 4877, 10133, 20399, 39881, 76085, 141877, 259373, 465493, 821813, 1428725, 2449573, 4145249, 6931259, 11459483, 18749007, 30373189, 48752125, 77568683, 122406223, 191651957, 297856813, 459652759, 704595749, 1073152385

Offset

0,2

Comments

A bisection of A341710.

Links

Table of n, a(n) for n=0..31.

D. Weigel, R. Veysseyre, T. Phan, J. M. Effantin, and Y. Billiet, Crystallography, geometry and physics in higher dimensions. I. Point-symmetry operations, Acta Cryst., A40 (1984), 323-330 (see Table 3).

Maple

with(numtheory):
b:= proc(n) option remember; nops(invphi(n)) end:
g:= proc(n) option remember; `if`(n=0, 1, add(
      g(n-j)*add(d*b(d), d=divisors(j)), j=1..n)/n)
    end:
a:= n-> g(2*n+1)/2:
seq(a(n), n=0..40);  # Alois P. Heinz, Feb 19 2021

Mathematica

terms = 64; (* number of terms of A120963 *)
nmax = Floor[terms/2] - 1;
S[m_] := S[m] = CoefficientList[Product[1/(1 - x^EulerPhi[k]),
     {k, 1, m*terms}] + O[x]^(terms + 1), x];
S[m = 1];
S[m++];
While[S[m] != S[m - 1], m++];
A120963 = S[m];
a[n_ /; 0 <= n <= nmax] := A120963[[2 n + 2]]/2;
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, May 12 2022 *)

Crossrefs

Cf. A120963, A341710, A341712.

Sequence in context: A107179 A332720 A092442 * A328543 A135266 A124123

Adjacent sequences: A341708 A341709 A341710 * A341712 A341713 A341714

Keyword

nonn

Author

N. J. A. Sloane, Feb 19 2021

Status

approved