|
Search: id:A098307
|
|
|
| A098307 |
|
Unsigned member r=-7 of the family of Chebyshev sequences S_r(n) defined in A092184. |
|
+0
1
|
|
| 0, 1, 7, 64, 567, 5041, 44800, 398161, 3538647, 31449664, 279508327, 2484125281, 22077619200, 196214447521, 1743852408487, 15498457228864, 137742262651287, 1224181906632721, 10879894897043200, 96694872166756081
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
((-1)^(n+1))*a(n) = S_{-7}(n), n>=0, defined in A092184.
|
|
LINKS
|
Index entries for sequences related to Chebyshev polynomials.
|
|
FORMULA
|
a(n)= 2*(T(n, 9/2)-(-1)^n)/11, with twice Chebyshev's polynomials of the first kind evaluated at x=9/2: 2*T(n, 9/2)=A056918(n)=((9+sqrt(77))^n + (9-sqrt(77))^n)/2^n.
a(n)= 9*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
a(n)= 8*a(n-1) + 8*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=7.
G.f.: x*(1-x)/((1+x)*(1-9*x+x^2)) = x*(1-x)/(1-8*x-8*x^2+x^3) (from the Stephan link, see A092184).
|
|
CROSSREFS
|
Sequence in context: A027767 A055537 A159617 this_sequence A055995 A008787 A024095
Adjacent sequences: A098304 A098305 A098306 this_sequence A098308 A098309 A098310
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004
|
|
|
Search completed in 0.002 seconds
|
