|
Search: id:A077239
|
|
|
| A077239 |
|
Bisection (odd part) of Chebyshev sequence with Diophantine property. |
|
+0
5
|
|
| 7, 37, 215, 1253, 7303, 42565, 248087, 1445957, 8427655, 49119973, 286292183, 1668633125, 9725506567, 56684406277, 330380931095, 1925601180293, 11223226150663, 65413755723685, 381259308191447, 2222142093424997
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
a(n)^2 - 8*b(n)^2 = 17, with the companion sequence b(n)= A077413(n).
The even part is A077240(n) with Diophantine companion A054488(n).
|
|
LINKS
|
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
|
|
FORMULA
|
a(n)= 6*a(n-1) - a(n-2), a(-1) := 5, a(0)=7.
a(n)= 2*T(n+1, 3)+T(n, 3), with T(n, x) Chebyshev's polynomials of the first kind, A053120. T(n, 3)= A001541(n).
G.f.: (7-5*x)/(1-6*x+x^2).
|
|
EXAMPLE
|
37 = a(1) = sqrt(8*A077413(1)^2 +17) = sqrt(8*13^2 + 17)= sqrt(1369) = 37.
|
|
CROSSREFS
|
Cf. A077242 (even and odd parts).
Sequence in context: A124610 A002683 A126475 this_sequence A046235 A144496 A025012
Adjacent sequences: A077236 A077237 A077238 this_sequence A077240 A077241 A077242
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 08 2002
|
|
|
Search completed in 0.002 seconds
|
