id:A106249 - OEIS Search Results

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Expansion of (1-x+x^2+x^3)/(1-x-x^4+x^5).

+0
4

1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 9, 10, 11, 10, 11, 12, 13, 12, 13, 14, 15, 14, 15, 16, 17, 16, 17, 18, 19, 18, 19, 20, 21, 20, 21, 22, 23, 22, 23, 24, 25, 24, 25, 26, 27, 26, 27, 28, 29, 28, 29, 30, 31, 30, 31, 32, 33, 32, 33, 34, 35, 34, 35, 36, 37, 36, 37, 38 (list; graph; listen)

	OFFSET	`0,4`
	FORMULA	`G.f.: (1-x+x^2+x^3)/(1-x-x^4+x^5)=(1+x^2+2x^3+x^4+2x^5+x^6)/(1-x^4)^2; a(n)=sum{k=0..n, -mu(k mod 4)}; a(n)=cos(pin/2)/2-sin(pin/2)/2+(-1)^n/4+(2n+1)/4.` `a(n)=sum{k=0..n, Jacobi(2^k, 2k+1)} [Conjecture]; - Paul Barry (pbarry(AT)wit.ie), Jul 23 2005` `a(n)=sum{k=0..n, Product{j=1..k, ((-1)^j)^(k-j+1)}}; - Paul Barry (pbarry(AT)wit.ie), Nov 09 2007`
	CROSSREFS	`Cf. A008611.` `Sequence in context: A095207 A065362 A083219 this_sequence A110516 A134986 A026342` `Adjacent sequences: A106246 A106247 A106248 this_sequence A106250 A106251 A106252`
	KEYWORD	`easy,nonn`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Apr 27 2005`

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.

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