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A054486
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Expansion of (1+2x)/(1-3x+x^2).
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7
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1, 5, 14, 37, 97, 254, 665, 1741, 4558, 11933, 31241, 81790, 214129, 560597, 1467662, 3842389, 10059505, 26336126, 68948873, 180510493, 472582606, 1237237325, 3239129369, 8480150782, 22201322977, 58123818149, 152170131470, 398386576261, 1042989597313
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A000285. - R. J. Mathar, Oct 26 2011
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REFERENCES
| I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7 (1969), pps. 181-193.
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 122-125, 194-196.
E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 7 (1969), pps. 231-242.
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LINKS
| Tanya Khovanova, Recursive Sequences
Index to sequences with linear recurrences with constant coefficients, signature (3,-1).
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FORMULA
| a(n)=3a(n-1)-a(n-2), a(0)=1, a(1)=5.
a(n) + 7*A001519(n) = A005248(n) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 30 2004
Lucas(2n+1) + Fibonacci(2n).
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EXAMPLE
| a(n)={5*([(3+sqrt(5))/2]^n-[(3-sqrt(5))/2]^n)-([(3+sqrt(5))/2]^(n-1)-[(3-sqrt(5))/2]^(n-1))}/sqrt(5).
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MATHEMATICA
| CoefficientList[Series[(2*z + 1)/(z^2 - 3*z + 1), {z, 0, 100}], z] (* From Vladimir Joseph Stephan Orlovsky, Jul 15 2011 *)
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PROG
| (PARI) Vec((1+2*x)/(1-3*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Jul 15 2011
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CROSSREFS
| Cf. A002878.
Sequence in context: A052951 A048745 A127980 * A072130 A196976 A045553
Adjacent sequences: A054483 A054484 A054485 * A054487 A054488 A054489
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, May 06 2000
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EXTENSIONS
| "a(1)=5", not "a(0)=5" Dan Nielsen (nielsed(AT)uah.edu), Sep 10 2009
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