|
Search: id:A086902
|
|
|
| A086902 |
|
a(n) = 7a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 7, a(n) = [(7+sqrt(53))/2]^n + [(7-sqrt(53))/2]^n. |
|
+0
2
|
|
| 2, 7, 51, 364, 2599, 18557, 132498, 946043, 6754799, 48229636, 344362251, 2458765393, 17555720002, 125348805407, 894997357851, 6390330310364, 45627309530399, 325781497023157, 2326097788692498, 16608466017870643
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
a(n+1)/a(n) converges to (7+sqrt(53))/2 = 7.14005... a(0)/a(1)=2/7; a(1)/a(2)=7/51; a(2)/a(3)=51/364; a(3)/a(4)=364/2599; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.1400549... = 2/(7+sqrt(53)) = (sqrt(53)-7)/2.
|
|
LINKS
|
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
Index entries for sequences related to Chebyshev polynomials.
|
|
FORMULA
|
a(n) = 7a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 7, a(n) = [(7+sqrt(53))/2]^n + [(7-sqrt(53))/2]^n.
E.g.f. : 2exp(7x/2)cosh(sqrt(53)x/2); a(n)=2^(1-n)sum{k=0..floor(n/2), C(n, 2k)53^k7^(n-2k)}. a(n)=2T(n, 7i/2)(-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.: (2-7x)/(1-7x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2008]
|
|
EXAMPLE
|
a(4) = 2599 = 7a(3) + a(2) = 7*364 + 51 = [(7+sqrt(53))/2]^4 + [(7-sqrt(53))/2]^4 =
2598.999615 + 0.000385 = 2599
|
|
CROSSREFS
|
Cf. A058316.
Sequence in context: A045598 A139008 A058721 this_sequence A138737 A046662 A118191
Adjacent sequences: A086899 A086900 A086901 this_sequence A086903 A086904 A086905
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 18 2003
|
|
EXTENSIONS
|
More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 14 2004
|
|
|
Search completed in 0.002 seconds
|
