A284711 Even bisection of A283848.

23, 86, 339, 1332, 5298, 21066, 83987, 334966, 1336988, 5338206, 21321234, 85176636, 340338398, 1360073016, 5435820051, 21727481616, 86853790498, 347214198246, 1388133456348, 5549915835836, 22190143855898, 88725807876186, 354775752246802, 1418633882621748, 5672803378074548

Offset: 2

Author

N. J. A. Sloane, Apr 01 2017

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 2..1659
• Shinsaku Fujita, alpha-beta Itemized Enumeration of Inositol Derivatives and m-Gonal Homologs by Extending Fujita's Proligand Method, Bull. Chem. Soc. Jpn. 2017, 90, 343-366; doi:10.1246/bcsj.20160369. See Table 8.

Crossrefs

The 8 sequences in Table 8 of Fujita (2017) are A053656, A000011, A256216, A256217, A123045, A283846, A283847, A283848.

The even bisection of A283848 gives A000079.

Programs

Maple

f:= proc(n) uses numtheory;
(4*n)^(-1)*add(phi(d)*4^(2*n/d),d=select(type,divisors(2*n),even))+5*2^(2*n-2)
end proc:
map(f, [$2..40]);

PARI

A(m,n) = if (m%2, 2^((m-1)/2)*n^((m+1)/2), sumdiv(m, d, ((d%2)==0)*(eulerphi(d)*2^(m/d)*n^(m/d)))/(2*m) + 2^(m/2-2)*n^(m/2)*(2*n+1));
lista(nn) = for(n=2, nn, print1(T(2*n, 2), ", ")) \\ Michel Marcus, Apr 02 2017

Formula

a(n) = A283848(2*n)=(4*n)^(-1)*Sum_{d|2*n, d even} phi(d)*4^(2*n/d) + 5*2^(2*n-2). - Robert Israel, Aug 23 2018 after Fujita (2017), Eq. (101)

Extensions

More terms from Michel Marcus, Apr 02 2017

Edited by Robert Israel, Aug 23 2018