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

2,1

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.

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)

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]);

Prog

(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

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.

Sequence in context: A010011 A172117 A217529 * A193018 A044210 A044591

Adjacent sequences: A284708 A284709 A284710 * A284712 A284713 A284714

Keyword

nonn

Author

N. J. A. Sloane, Apr 01 2017

Extensions

More terms from Michel Marcus, Apr 02 2017

Edited by Robert Israel, Aug 23 2018

Status

approved