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A088320 a(n) = 10a(n-1) + a(n-2), starting with a(0) = 1 and a(1) = 5. 1
1, 5, 51, 515, 5201, 52525, 530451, 5357035, 54100801, 546365045, 5517751251, 55723877555, 562756526801, 5683289145565, 57395647982451, 579639768970075, 5853793337683201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

LINKS

Table of n, a(n) for n=0..16.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (10, 1).

Index entries for sequences related to Chebyshev polynomials.

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, Nov 15 2003

G.f. : (1-5x)/(1-10x-x^2). [From R. J. Mathar, Sep 11 2008]

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.

CROSSREFS

Cf. A041043, A064019, A077392.

Cf. A041040. [From R. J. Mathar, Sep 11 2008]

Sequence in context: A195211 A106415 A212819 * A041040 A223002 A180511

Adjacent sequences:  A088317 A088318 A088319 * A088321 A088322 A088323

KEYWORD

easy,nonn

AUTHOR

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Nov 06 2003

STATUS

approved

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Last modified August 20 22:48 EDT 2017. Contains 290837 sequences.