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A056014
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(Fibonacci(2n-1)-Fibonacci(n+1))/2 .
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4
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0, 0, 0, 1, 4, 13, 38, 106, 288, 771, 2046, 5401, 14212, 37324, 97904, 256621, 672336, 1760997, 4611642, 12075526, 31617520, 82781215, 216732890, 567428401, 1485570024, 3889310328, 10182407328, 26657986681, 69791674108
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| With a(0)=0, a(1)=1, a(2)=1, a(3)=2, this recurrence produces a(n)=A000045(n) (Fibonacci numbers).
Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 5 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 1, s(n) = 4. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 16 2004
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (4,-3,-2,1)
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FORMULA
| a(n)=4a(n-1)-3a(n-2)-2a(n-3)+a(n-4), a(0)=a(1)=a(2)=0, a(3)=1.
Convolution of Fibonacci numbers F(n) with F(2n). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 07 2004
G.f.: x^3/((1-x-x^2)*(1-3*x+x^2)) - Herbert Kociemba (kociemba(AT)t-online.de), Jun 16 2004
Binomial transform of x^3/(1-3x^2+x^4), or (essentially) F(2n) with interpolated zeros. a(n)=sum{k=0..n, binomial(n, k)((3/2-sqrt(5)/2)^(k/2)((sqrt(5)/20+1/4)(-1)^k-sqrt(5)/20-1/4)+ (sqrt(5)/2+3/2)^(k/2)((sqrt(5)/20-1/4)(-1)^k-sqrt(5)/20+1/4))} - Paul Barry (pbarry(AT)wit.ie), Jul 26 2004
Convolution of the powers of 2 (A000079) with the number of positive rational knots with 2n+1 crossings (A051450), with three leading zeros. - Graeme McRae (g_m(AT)mcraefamily.com), Jun 28 2006
a(n) = (A001519(n)-A000045(n+1))/2. - R. J. Mathar, Jun 24 2011
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MATHEMATICA
| Table[(Fibonacci[2n-1]-Fibonacci[n+1])/2, {n, 0, 40}] (* From Harvey P. Dale, Mar 24 2011 *)
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PROG
| (PARI) a(n)=(fibonacci(2*n-1)-fibonacci(n+1))/2
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CROSSREFS
| Cf. A000045, A056015.
a(1-2n)=A059512(2n), a(-2n)=A027994(2n-1).
Sequence in context: A049611 A084851 A094706 * A159036 A058693 A027076
Adjacent sequences: A056011 A056012 A056013 * A056015 A056016 A056017
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KEYWORD
| nonn,easy
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AUTHOR
| Asher Auel (asher.auel(AT)reed.edu), Jun 06 2000
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