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A099254
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Self-convolution of A010892. The g.f. is 1/(Alexander polynomial of granny knot).
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10
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| A granny knot sequence.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,-3,2,-1)
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FORMULA
| G.f.: 1/(1-2x+3x^2-2x^3+x^4)=1/(1-x+x^2)^2; a(n)=4sqrt(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 (pbarry(AT)wit.ie), Nov 12 2004
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CROSSREFS
| Row sums of array A128502.
Sequence in context: A119538 A068309 A186731 * A099470 A180108 A121339
Adjacent sequences: A099251 A099252 A099253 * A099255 A099256 A099257
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 08 2004
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