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A084179
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A Fibonacci related expansion.
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1
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0, 1, -1, 4, -5, 15, -22, 57, -93, 220, -385, 859, -1574, 3381, -6385, 13380, -25773, 53143, -103702, 211585, -416405, 843756, -1669801, 3368259, -6690150, 13455325, -26789257, 53774932, -107232053, 214978335, -429124630, 859595529, -1717012749, 3437550076
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Sums of consecutive pairs yield A083178.
Number of walks of length n+1 between two vertices at distance 2 in the cycle graph C_5. In general a(n,m)=2^n/m*Sum(k,0,m-1,Cos(4Pi*k/m)Cos(2Pi*k/m)^n) is the number of walks of length n between two vertices at distance 2 in the cycle graph C_m. - Herbert Kociemba (kociemba(AT)t-online.de), May 31 2004
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FORMULA
| G.f.: x/((1+2x)(1-x-x^2))
Binomial transform is A007598. The unsigned sequence has G.f. x/((1-2x)(1+x-x^2)) with a(n)=2*2^n/5-(-1)^n*A000032(n)/5. - Paul Barry (pbarry(AT)wit.ie), Apr 17 2004
a(n)=sum{k=0..n, (-1)^(n-k)C(n, k)Fib(k)^2 }; a(n)=((1/2-sqrt(5)/2)^n+(1/2+sqrt(5)/2)^n-2(-2)^n)/5; a(n)=A000032(n)/5-2(-2)^n/5. - Paul Barry (pbarry(AT)wit.ie), Apr 17 2004
a(n)=2^n/5*Sum(k, 0, 4, Cos(4Pi*k/5)Cos(2Pi*k/5)^n) - Herbert Kociemba (kociemba(AT)t-online.de), May 31 2004
a(n)=-a(n-1)+3a(n-2)+2a(n-3). - Paul Curtz (bpcrtz(AT)free.fr), Mar 09 2008
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CROSSREFS
| Sequence in context: A100234 A007390 A037955 * A026634 A026656 A184244
Adjacent sequences: A084176 A084177 A084178 * A084180 A084181 A084182
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 18 2003
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