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A090300 a(n) = 14*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14. 14
2, 14, 198, 2786, 39202, 551614, 7761798, 109216786, 1536796802, 21624372014, 304278004998, 4281516441986, 60245508192802, 847718631141214, 11928306344169798, 167844007449518386, 2361744410637427202 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
a(n+1)/a(n) converges to (7+sqrt(50)) = 14.071067811...
Lim_{n->infinity} a(n)/a(n+1) = 0.071067811... = 1/(7+sqrt(50)) = sqrt(50) - 7.
Lim_{n->infinity} a(n+1)/a(n) = 14.071067811... = (7+sqrt(50)) = 1/(sqrt(50) - 7).
LINKS
Tanya Khovanova, Recursive Sequences
FORMULA
a(n) = 14*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14.
a(n) = (7+sqrt(50))^n + (7-sqrt(50))^n.
(a(n))^2 = a(2n)-2 if n = 1, 3, 5, ...; (a(n))^2 = a(2n)+2 if n = 2, 4, 6, ....
G.f.: (2-14*x)/(1-14*x-x^2). - Philippe Deléham, Nov 02 2008
EXAMPLE
a(4) = 39202 = 14*a(3) + a(2) = 14*2786 + 198 = (7+sqrt(50))^4 + (7-sqrt(50))^4 = 39201.999974491 + 0.000025508 = 39202.
MATHEMATICA
LinearRecurrence[{14, 1}, {2, 14}, 20] (* Harvey P. Dale, Jul 12 2020 *)
CROSSREFS
Cf. A050012.
Sequence in context: A232686 A263766 A244577 * A213977 A322196 A102224
KEYWORD
easy,nonn
AUTHOR
Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 25 2004
EXTENSIONS
More terms from Ray Chandler, Feb 14 2004
STATUS
approved

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Last modified July 15 16:08 EDT 2024. Contains 374333 sequences. (Running on oeis4.)