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A054490
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Expansion of (1+5x)/(1-6x+x^2).
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5
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1, 11, 65, 379, 2209, 12875, 75041, 437371, 2549185, 14857739, 86597249, 504725755, 2941757281, 17145817931, 99933150305, 582453083899, 3394785353089, 19786259034635, 115322768854721, 672150354093691
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A Pellian-related second order recursive sequence.
Binomial transform of A164607. - 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 (6,-1).
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FORMULA
| a(n)=6a(n-1)-a(n-2), a(0)=1, a(1)=11.
a(n) = sqrt{8*(A038723)^2-7}
a(n)={11*([3+2sqrt(2)]^n-[3-2sqrt(2)]^n)-([3+2sqrt(2)]^(n-1)-[3-2sqrt(2)]^(n-1))}/4sqrt(2).
a(n)=third binomial transform of 1,8,8,64,64,512 [From Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009]
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MAPLE
| a[0]:=1: a[1]:=11: for n from 2 to 26 do a[n]:=6*a[n-1]-a[n-2] od: seq(a[n], n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 26 2006
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CROSSREFS
| Cf. A054488, A054489, A038723.
Sequence in context: A054333 A036601 A125321 * A126479 A139611 A154617
Adjacent sequences: A054487 A054488 A054489 * A054491 A054492 A054493
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, May 04 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 05 2000
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