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A099254 Self-convolution of A010892. The g.f. is 1/(Alexander polynomial of granny knot). 15
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A granny knot sequence.

INVERTi transform of A077855: (1, 3, 6, 11, 20, 36, 64, 133, ...). - Gary W. Adamson, Jan 13 2017

LINKS

Table of n, a(n) for n=0..62.

Index entries for linear recurrences with constant coefficients, signature (2,-3,2,-1)

FORMULA

G.f.: 1/(1-2*x+3*x^2-2*x^3+x^4) = 1/(1-x+x^2)^2.

a(n) = 4*sqrt(3)*sin(Pi*n/3+Pi/3)/9+2*(n + 1)*sin(Pi*n/3+Pi/6)/3.

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)*(n-k+1)*(-1)^k. - Paul Barry, Nov 12 2004

a(n) = 2*cos(2*Pi*(n+2)/3)*(floor(n/3)+1)*(-1)^(n+1). - Tani Akinari, Jul 01 2013

a(n) = 1/54*(18(n + 2)*(-1)^floor(n/3) + (3n + 11)*(-1)^floor((n + 1)/3) - 9(n + 1)*(-1)^floor((n + 2)/3) - 2(3n + 8)*(-1)^floor((n + 4)/3)). - John M. Campbell, Dec 23 2016

CROSSREFS

Row sums of array A128502.

Cf. A077855.

Sequence in context: A119538 A068309 A099470 * A186731 A180108 A121339

Adjacent sequences:  A099251 A099252 A099253 * A099255 A099256 A099257

KEYWORD

easy,sign

AUTHOR

Paul Barry, Oct 08 2004

STATUS

approved

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Last modified September 26 01:25 EDT 2017. Contains 292500 sequences.