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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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