id:A099254 - OEIS Search Results

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Self-convolution of A010892. The g.f. is 1/(Alexander polynomial of granny knot).

+0
5

1, 2, 1, -2, -4, -2, 3, 6, 3, -4, -8, -4, 5, 10, 5, -6, -12, -6, 7, 14, 7, -8, -16, -8, 9, 18, 9, -10, -20, -10, 11, 22, 11, -12, -24, -12, 13, 26, 13, -14, -28, -14, 15, 30, 15, -16, -32, -16, 17, 34, 17, -18, -36, -18, 19, 38, 19, -20, -40, -20, 21, 42, 21 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`A granny knot sequence.`
	FORMULA	`G.f.: 1/(1-2x+3x^2-2x^3+x^4)=1/(1-x+x^2)^2; a(n)=4sqrt(3)sin(pin/3+pi/3)/9+2(n + 1)sin(pin/3+pi/6)/3.` `a(n)=sum{k=0..floor(n/2), binomial(n-k,k)(n-k+1)*(-1)^k}. - Paul Barry (pbarry(AT)wit.ie), Nov 12 2004`
	CROSSREFS	`Row sums of array A128502.` `Sequence in context: A119538 A068309 A099470 this_sequence A121339 A099500 A120253` `Adjacent sequences: A099251 A099252 A099253 this_sequence A099255 A099256 A099257`
	KEYWORD	`easy,sign`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Oct 08 2004`

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.

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