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

%I A000570 #39 Jul 02 2025 16:01:53
%S A000570 1,1,2,4,7,11,18,31,53,89,149,251,424,715,1204,2028,3418,5761,9708,
%T A000570 16358,27565,46452,78279,131910,222285,374581,631222,1063696,1792472,
%U A000570 3020560,5090059,8577449,14454177,24357268,41045336,69167021,116555915
%N A000570 Number of tournaments on n nodes determined by their score vectors.
%C A000570 a(n+1) is the number of multus bitstrings of length n with no runs of 5 ones. - _Steven Finch_, Mar 25 2020
%H A000570 T. D. Noe, <a href="/A000570/b000570.txt">Table of n, a(n) for n = 1..500</a>
%H A000570 Steven Finch, <a href="https://arxiv.org/abs/2003.09458">Cantor-solus and Cantor-multus distributions</a>, arXiv:2003.09458 [math.CO], 2020.
%H A000570 Prasad Tetali, <a href="https://doi.org/10.1006/jctb.1997.1799">A characterization of unique tournaments</a>, J. Comb Theory B 72 (1) (1998), 157-159.
%H A000570 <a href="/index/To#tournament">Index entries for sequences related to tournaments</a>
%H A000570 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,1,1).
%F A000570 a(n) = a(n-5) + a(n-4) + a(n-3) + a(n-1). - _Jon E. Schoenfield_, Aug 07 2006
%F A000570 G.f.: (1+x^2+x^3+x^4)/(1-x-x^3-x^4-x^5). - _Harvey P. Dale_, May 05 2011
%p A000570 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;
%t A000570 LinearRecurrence[{1,0,1,1,1},{1,1,2,4,7},50] (* _Harvey P. Dale_, May 05 2011 *)
%o A000570 (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
%K A000570 nonn,nice,easy
%O A000570 1,3
%A A000570 Prasad Tetali [ tetali(AT)math.gatech.edu ]
%E A000570 More terms from _James Sellers_, Feb 06 2000