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A105371 Expansion of (1-x)(1-x+x^2)/(1-3x+4x^2-2x^3+x^4). 7
1, 1, 1, 0, -3, -8, -13, -13, 0, 34, 89, 144, 144, 0, -377, -987, -1597, -1597, 0, 4181, 10946, 17711, 17711, 0, -46368, -121393, -196418, -196418, 0, 514229, 1346269, 2178309, 2178309, 0, -5702887, -14930352, -24157817, -24157817, 0, 63245986, 165580141 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Binomial transform of A105367.

LINKS

Table of n, a(n) for n=0..40.

Index entries for two-way infinite sequences

Index entries for linear recurrences with constant coefficients, signature (3,-4,2,-1)

FORMULA

G.f. : (1-2x+2x^2-x^3)/(1-3x+4x^2-2x^3+x^4); a(n)=3a(n-1)-4a(n-2)+2a(n-3)-a(n-4); (1/2+sqrt(5)/2)^n((1/2+sqrt(5)/10)cos(Pi*n/5)+sqrt(1/10-sqrt(5)/50)sin(Pi*n/5))- (sqrt(5)/2-1/2)^n((sqrt(5)/10-1/2)cos(2*Pi*n/5)+sqrt(1/10+sqrt(5)/50)sin(2*Pi*n/5))

a(5n)=-F(-5n-1), a(5n+1)=a(5n+2)=-F(-5n-2), a(5n+3)=0, a(5n+4)=F(-5n-4). - Michael Somos, Apr 09 2005

MATHEMATICA

CoefficientList[Series[(1-x)(1-x+x^2)/(1-3x+4x^2-2x^3+x^4), {x, 0, 60}], x] (* or *) LinearRecurrence[{3, -4, 2, -1}, {1, 1, 1, 0}, 60] (* Harvey P. Dale, Dec 21 2013 *)

PROG

(PARI) a(n)=local(m); m=n%5+1; [1, -1, -1, 0, 1][m]*fibonacci(-n-(m<3)) /* Michael Somos, Apr 09 2005 */

CROSSREFS

Cf. A000045.

Sequence in context: A218889 A131213 A320260 * A038188 A310285 A310286

Adjacent sequences:  A105368 A105369 A105370 * A105372 A105373 A105374

KEYWORD

easy,sign

AUTHOR

Paul Barry, Apr 01 2005

STATUS

approved

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Last modified May 23 12:38 EDT 2019. Contains 323514 sequences. (Running on oeis4.)