The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A188697 Expansion of (1+2*x^2)/(1-26*x+2*x^2-52*x^3+4*x^4). 1
1, 26, 676, 17576, 456972, 11881168, 308907672, 8031529376, 208817941280, 5429219088800, 141158464323104, 3670088041052160, 95421456259562432, 2480936209934965120, 64503778490067388160, 1677083603695215199744, 43603793136187040353536, 1133688727070116383116288, 29475649649828842801150464, 766360202350076625301264384 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
From the Noonan and Zeilberger link below, a(n) is the number of words in the 26-letter English alphabet {A,B,C,...,X,Y,Z} that do not contain any of the "bad" words: PIPI or CACA or PICA or CAPI. The expected wait time to see an occurrence of one of any of these four words is G(1/26) = 114582. The expected wait time to see all four of these words is 979223595402/1028195 (approximately 952371). - Geoffrey Critzer, May 17 2014
LINKS
FORMULA
G.f.: (1+2*x^2)/(1-26*x+2*x^2-52*x^3+4*x^4).
a(0)=1, a(1)=26, a(2)=676, a(3)=17576, a(n)=26*a(n-1)-2*a(n-2)+ 52*a(n-3)- 4*a(n-4). - Harvey P. Dale, Oct 04 2014
MATHEMATICA
sol=Solve[{A==-z^4-z^2A-z^2D, B==-z^4-z^2B-z^2C, C==-z^4-z^2A-z^2D, D==-z^4-z^2B-z^2C}, {A, B, C, D}]; nn=20; CoefficientList[Series[1/(1-26z-A-B-C-D)/.sol, {z, 0, nn}], z] (* Geoffrey Critzer, May 17 2014 *)
LinearRecurrence[{26, -2, 52, -4}, {1, 26, 676, 17576}, 30] (* Harvey P. Dale, Oct 04 2014 *)
CROSSREFS
Cf. A188696.
Sequence in context: A206695 A171300 A360509 * A188696 A009970 A041313
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 08 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)