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A088320
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a(n) = 10a(n-1) + a(n-2), starting with a(0) = 1 and a(1) = 5.
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1
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1, 5, 51, 515, 5201, 52525, 530451, 5357035, 54100801, 546365045, 5517751251, 55723877555, 562756526801, 5683289145565, 57395647982451, 579639768970075, 5853793337683201
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n+1)/a(n) converges to (5+sqrt(26)) =10.099019... a(0)/a(1)=1/5; a(1)/a(2)=5/51; a(2)/a(3)=51/515; a(3)/a(4)=515/5201; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.099019... = 1/(5+sqrt(26)) = (sqrt(26)-5).
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LINKS
| Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n) = 10a(n-1) + a(n-2), starting with a(0) = 1 and a(1) = 5. a(n) = a(n) = ((5+sqrt(26))^n + (5-sqrt(26))^n)/2. a(n) = A086927(n)/2
E.g.f. : exp(5x)cosh(sqrt(26)x); a(n)=sum{k=0..floor(n/2), C(n, 2k)26^k5^(n-2k)}. a(n)=T(n, 5i)(-i)^n with T(n, x) Chebyshev's polynomials of the first kind (see A053120) and i^2=-1. - Paul Barry (pbarry(AT)wit.ie), Nov 15 2003
G.f. : (1-5x)/(1-10x-x^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 11 2008]
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EXAMPLE
| a(4) = 5201 = 10a(3) + a(2) = 10*515 + 51 = ((5+sqrt(26))^4 + (5-sqrt(26))^4)/2 = (10401.999903 + 0.000097)/2 = 5201.
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CROSSREFS
| Cf. A041043, A064019, A077392.
Cf. A041040. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 11 2008]
Sequence in context: A145641 A195211 A106415 * A041040 A180511 A190734
Adjacent sequences: A088317 A088318 A088319 * A088321 A088322 A088323
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KEYWORD
| easy,nonn
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AUTHOR
| Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Nov 06 2003
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