login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000570 Number of tournaments on n nodes determined by their score vectors. 4
1, 1, 2, 4, 7, 11, 18, 31, 53, 89, 149, 251, 424, 715, 1204, 2028, 3418, 5761, 9708, 16358, 27565, 46452, 78279, 131910, 222285, 374581, 631222, 1063696, 1792472, 3020560, 5090059, 8577449, 14454177, 24357268, 41045336, 69167021, 116555915 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n+1) is the number of multus bitstrings of length n with no runs of 5 ones. - Steven Finch, Mar 25 2020

LINKS

T. D. Noe, Table of n, a(n) for n = 1..500

Steven Finch, Cantor-solus and Cantor-multus distributions, arXiv:2003.09458 [math.CO], 2020.

Prasad Tetali, A characterization of unique tournaments, J. Comb Theory B 72 (1) (1998), 157-159.

Index entries for sequences related to tournaments

Index entries for linear recurrences with constant coefficients, signature (1,0,1,1,1).

FORMULA

a(n) = a(n-5) + a(n-4) + a(n-3) + a(n-1). - Jon E. Schoenfield, Aug 07 2006

G.f.: (1+x^2+x^3+x^4)/(1-x-x^3-x^4-x^5). - Harvey P. Dale, May 05 2011

MAPLE

A000570 := proc(n) option remember; if n <= 2 then RETURN(1) elif n=3 then RETURN(2) elif n=4 then RETURN(4) elif n=5 then RETURN(7) else A000570(n-1)+A000570(n-3)+A000570(n-4)+A000570(n-5); fi; end;

MATHEMATICA

LinearRecurrence[{1, 0, 1, 1, 1}, {1, 1, 2, 4, 7}, 50] (* Harvey P. Dale, May 05 2011 *)

PROG

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, 1, 1, 0, 1]^(n-1)*[1; 1; 2; 4; 7])[1, 1] \\ Charles R Greathouse IV, Jun 15 2015

CROSSREFS

Sequence in context: A228560 A018063 A289004 * A239552 A023426 A157134

Adjacent sequences:  A000567 A000568 A000569 * A000571 A000572 A000573

KEYWORD

nonn,nice,easy

AUTHOR

Prasad Tetali [ tetali(AT)math.gatech.edu ]

EXTENSIONS

More terms from James A. Sellers, Feb 06 2000

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 27 01:55 EDT 2020. Contains 337379 sequences. (Running on oeis4.)