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A284711
Even bisection of A283848.
2
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
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
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