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%I #14 Mar 12 2021 22:24:42
%S 1,0,0,0,0,1,2,3,5,7,9,12,15,18,22,26,30,35,40,45,51,57,63,70,77,84,
%T 92,100,108,117,126,135,145,155,165,176,187,198,210,222,234,247,260,
%U 273,287,301,315,330,345,360,376,392,408,425,442,459,477,495,513,532,551
%N Maximal exponent of x in all terms of Somos polynomial of order n.
%C This sequence differs from A001840 only in four terms preceding it. That is, A001840(n) = a(n+5).
%C Let b(n) = 2^a(n+1). Then b(1)=b(2)=b(3)=b(4)=1 and b(n)*b(n-4) = b(n-1)*b(n-3) + c(n)*b(n-2)^2, c(3*n)=2, c(3*n+1)=c(3*n+2)=1 for all n in Z. - _Michael Somos_, Oct 18 2018
%H Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/somospol.html">Somos Polynomials</a>
%F a(n) = 1 + a(n-1) + a(n-3) - a(n-4) for all n in Z.
%F G.f.: x*(1-2*x+x^2-x^3+2*x^4)/((1+x+x^2)* (1-x)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009
%F a(n) = a(7-n) for all n in Z. - _Michael Somos_, Oct 18 2018
%t e[1] = 1; e[2] = e[3] = e[4] = e[5] = 0; e[n_] := e[n] = 1 + e[n - 1] + e[n - 3] - e[n - 4]; Table[e[n], {n, 1, 70}]
%t a[ n_] := Quotient[ Binomial[n - 3, 2], 3]; (* _Michael Somos_, Oct 18 2018 *)
%o (Sage) [floor(binomial(n,2)/3) for n in range(-2,59)] # _Zerinvary Lajos_, Dec 01 2009
%o (PARI) {a(n) = binomial(n-3, 2)\3}; /* _Michael Somos_, Oct 18 2018 */
%Y Cf. A001840.
%K nonn
%O 1,7
%A _Robert G. Wilson v_, Jan 11 2001
%E G.f. proposed by Maksym Voznyy checked and corrected by _R. J. Mathar_, Sep 16 2009
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