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A002320 a(n) = 5*a(n-1) - a(n-2). 6
1, 3, 14, 67, 321, 1538, 7369, 35307, 169166, 810523, 3883449, 18606722, 89150161, 427144083, 2046570254, 9805707187, 46981965681, 225104121218, 1078538640409, 5167589080827, 24759406763726, 118629444737803 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Together with A002310 these are the two sequences satisfying ( a(n)^2+a(n-1)^2 )/(1 - a(n)a(n-1)) is an integer, in both cases this integer is -5. - Floor van Lamoen, Oct 26 2001

REFERENCES

From a posting to Netnews group sci.math by ksbrown(AT)seanet.com (K. S. Brown) on Aug 15 1996.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

MathPages, N = (x^2 + y^2)/(1+xy) is a Square

Index entries for linear recurrences with constant coefficients, signature (5,-1).

FORMULA

Sequences A002310, A002320 and A049685 have this in common: each one satisfies a(n+1) = (a(n)^2+5)/a(n-1) - Graeme McRae, Jan 30 2005

G.f.: (1-2x)/(1-5x+x^2). [From Philippe Deléham, Nov 16 2008]

a(n)=-(1/42)*sqrt(21)*[(5/2)-(1/2)*sqrt(21)]^n+(1/42)*[(5/2)+(1/2)*sqrt(21)]^n*sqrt(21)+(1/2)*[(5/2) +(1/2)*sqrt(21)]^n+(1/2)*[(5/2)-(1/2)*sqrt(21)]^n, with n>=0 [From Paolo P. Lava, Nov 21 2008]

a(n) = Sum_{k = 0..n} A238731(n,k)*2^k. - _Philippe Deléham, Mar 05 2014

MATHEMATICA

LinearRecurrence[{5, -1}, {1, 3}, 30] (* Harvey P. Dale, Nov 13 2014 *)

PROG

(Haskel)

a002320 n = a002320_list !! n

a002320_list = 1 : 3 :

   (zipWith (-) (map (* 5) (tail a002320_list)) a002320_list)

-- Reinhard Zumkeller, Oct 16 2011

CROSSREFS

Cf. A054477.

Sequence in context: A034275 A240008 A151322 * A151323 A181662 A241478

Adjacent sequences:  A002317 A002318 A002319 * A002321 A002322 A002323

KEYWORD

nonn,easy

AUTHOR

Joe Keane (jgk(AT)jgk.org)

STATUS

approved

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Last modified November 20 12:29 EST 2017. Contains 294971 sequences.