%I M3305 #30 Oct 18 2022 14:59:36
%S 1,4,7,12,16,23,28,35,40,47,52,59,64,71,76,83,88,95,100,107,112,119,
%T 124,131,136,143,148,155,160,167,172,179,184,191,196,203,208,215,220,
%U 227,232,239,244,251,256,263,268,275,280,287,292,299,304
%N Davenport-Schinzel numbers of degree n on 4 symbols.
%D R. K. Guy, Unsolved Problems in Number Theory, E20.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D R. G. Stanton and P. H. Dirksen, Davenport-Schinzel sequences, Ars. Combin., 1 (1976), 43-51.
%H R. G. Stanton and P. H. Dirksen, <a href="/A002004/a002004.pdf">Davenport-Schinzel sequences</a>, Ars. Combin., 1 (1976), 43-51. [Annotated scanned copy]
%H R. G. Stanton and P. H. Dirksen, <a href="/A002004/a002004_1.pdf">Davenport-Schinzel sequences</a>, Ars. Combin., 1 (1976), 43-51. [Annotated scanned copy, different annotations from one above]
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F For n > 4, a(2*n) = 12 * n - 13 and a(2*n+1) = 12 * n - 14. - _Sean A. Irvine_, Feb 19 2016
%F From _Chai Wah Wu_, Jun 17 2020: (Start)
%F a(n) = a(n-1) + a(n-2) - a(n-3) for n > 7.
%F G.f.: x*(x^2 + x + 1)*(x^4 + x^3 - x^2 + 2*x + 1)/((x - 1)^2*(x + 1)). (End)
%t LinearRecurrence[{1,1,-1},{1,4,7,12,16,23,28},60] (* _Harvey P. Dale_, Jul 22 2021 *)
%Y A row of the array in A259874.
%K nonn,nice,easy
%O 1,2
%A _N. J. A. Sloane_
%E Title improved and more terms from _Sean A. Irvine_, Feb 19 2016