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A097134
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3*Fibonacci(2n)+0^n.
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3
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1, 3, 9, 24, 63, 165, 432, 1131, 2961, 7752, 20295, 53133, 139104, 364179, 953433, 2496120, 6534927, 17108661, 44791056, 117264507, 307002465, 803742888, 2104226199, 5508935709, 14422580928, 37758807075, 98853840297, 258802713816
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A097133.
Image of 1/(1-3x) under the mapping g(x)->g(x/(1+x^2)) - Paul Barry (pbarry(AT)wit.ie), Jan 16 2005
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-1).
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FORMULA
| G.f.: (1+x^2)/(1-3x+x^2); a(n)=3a(n-1)-a(n-2), n>2; a(n)=sum{k=0..n, binomial(n, k)(3*Fibonacci(k)+(-1)^k)}; a(n)=A097135(2n).
a(n)=sum{k=0..floor(n/2), binomial(n-k-1)(-1)^k*3^(n-2k)} - Paul Barry (pbarry(AT)wit.ie), Jan 16 2005
a(n) = Fibonacci(n+2)^2 - Fibonacci(n-2)^2 [From Gary Detlefs, Dec 03 2010]
a(n)= Fibonacci(6*n)-5*Fibonacci(2*n)^3,n>0.[From Gary Detlefs, Oct 18 2011]
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PROG
| (MAGMA) [3*Fibonacci(2*n)+0^n: n in [0..30]]; // Vincenzo Librandi, Apr 21 2011
(PARI) a(n)=3*fibonacci(n+n)+0^n \\ Charles R Greathouse IV, Oct 18 2011
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CROSSREFS
| Cf. A000045.
Sequence in context: A090400 A123888 A166290 * A123892 A064831 A153582
Adjacent sequences: A097131 A097132 A097133 * A097135 A097136 A097137
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 26 2004
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