A000570 Number of tournaments on n nodes determined by their score vectors.

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

Offset: 1

Author

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

Keywords

• nonn
• nice
• easy

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).

Programs

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 *)

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

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

Extensions

More terms from James Sellers, Feb 06 2000