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A054477
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A Pellian-related sequence.
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4
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1, 13, 64, 307, 1471, 7048, 33769, 161797, 775216, 3714283, 17796199, 85266712, 408537361, 1957420093, 9378563104, 44935395427, 215298414031, 1031556674728, 4942484959609, 23680868123317, 113461855656976
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| A. F. Horadam, Pell Identities, Fib. Quart., Vol. 9, No. 3, 1971, pps. 245-252.
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 256.
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(n)=5a(n-1)-a(n-2); a(0)=1, a(1)=13.
(A054477)=sqrt{21*(A002320)^2-20}; where the algebraic operations on (A------) are performed from the inside - out; that is, first squared, then multiplied by 21, then 20 is subtracted and finally the square root is performed term-by-term.
G.f.: (1+8*x)/(1-5*x+x^2) [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 07 2008]
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MAPLE
| a := n-> (Matrix([[1, -8]]). Matrix([[5, 1], [ -1, 0]])^(n))[1, 1]; seq (a(n), n=0..20); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 07 2008]
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PROG
| (Haskel)
a054477 n = a054477_list !! n
a054477_list = 1 : 13 :
(zipWith (-) (map (* 5) (tail a054477_list)) a054477_list)
-- Reinhard Zumkeller, Oct 16 2011
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CROSSREFS
| Cf. A002320.
Sequence in context: A092653 A067465 A166605 * A169883 A010820 A022705
Adjacent sequences: A054474 A054475 A054476 * A054478 A054479 A054480
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, Apr 16 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 16 2000
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