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

1,3

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