|
Search: id:A057091
|
|
|
| A057091 |
|
Scaled Chebyshev U-polynomials evaluated at i*sqrt(2). Generalized Fibonacci sequence. |
|
+0
6
|
|
| 1, 8, 72, 640, 5696, 50688, 451072, 4014080, 35721216, 317882368, 2828828672, 25173688320, 224020135936, 1993550594048, 17740565839872, 157872931471360, 1404907978489856, 12502247279689728, 111257242065436672
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
a(n) gives the length of the word obtained after n steps with the substitution rule 0->1^8, 1->(1^8)0, starting from 0. The number of 1's and 0's of this word is 8*a(n-1) and 8*a(n-2), resp.
|
|
REFERENCES
|
A. F. Horadam, Special properties of the sequence W_n(a,b; p,q), Fib. Quart., 5.5 (1967), 424-434. Case n->n+1, a=0,b=1; p=8, q=8.
W. Lang, On polynomials related to powers of the generating function of Catalan's numbers, Fib. Quart. 38,5 (2000) 408-419; Eqs.(39) and (45),rhs, m=8.
|
|
LINKS
|
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
|
|
FORMULA
|
a(n) = 8*(a(n-1)+a(n-2)), a(-1)=0, a(0)=1.
a(n)= S(n, i*2*sqrt(2))*(-i*2*sqrt(2))^n with S(n, x) := U(n, x/2), Chebyshev's polynomials of the 2nd kind, A049310.
G.f.: 1/(1-8*x-8*x^2).
a(n)=Sum_{k, 0<=k<=n}7^k*A063967(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2006
|
|
CROSSREFS
|
Adjacent sequences: A057088 A057089 A057090 this_sequence A057092 A057093 A057094
Sequence in context: A111919 A052379 A062541 this_sequence A055275 A115970 A078995
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Aug 11 2000
|
|
|
Search completed in 0.002 seconds
|
