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A131456 Number of q-partial fraction summands of the reciprocal of n-th cyclotomic polynomial. +0
1
1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 8, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 7, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 10, 1, 2, 1, 2, 1, 2, 1, 2, 7 (list; graph; listen)
OFFSET

1,2

COMMENT

Let Phi(n,q) be the n-th cyclotomic polynomial in q. The q-partial fraction decomposition of 1/Phi(n,q) is a representation of 1/Phi(n,q) as a finite sum of functions v(q)/(1-q^m)^t, such that m<=n, and degree(v)<phi(m) (Euler's totient function A000010).

REFERENCES

A. O. Munagi, Computation of q-Partial Fractions, INTEGERS: Electronic Journal of Combinatorial Number Theory 7 (2007), #25.

LINKS

A. O. Munagi, Computation of q-Partial Fractions

Eric Weisstein's World of Mathematics, Cyclotomic Polynomial

EXAMPLE

(i) a(3)=1 because 1/Phi(3,q)=(1-q)/(1-q^3);

(ii) a(6)=2 because 1/Phi(6,q)=(-1-q)/(1-q^3) + (2+2q)/(1-q^6).

CROSSREFS

Cf. A051664 A051664 Number of terms in n-th cyclotomic polynomial.

Sequence in context: A078313 A025827 A025826 this_sequence A074944 A065031 A058061

Adjacent sequences: A131453 A131454 A131455 this_sequence A131457 A131458 A131459

KEYWORD

nonn

AUTHOR

Augustine O. Munagi (amunagi(AT)yahoo.com), Jul 12 2007

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Last modified August 29 17:54 EDT 2008. Contains 143238 sequences.


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