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A058937 Maximal exponent of x in all terms of Somos polynomial of order n. 4

%I

%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 M. 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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Last modified January 24 22:09 EST 2021. Contains 340414 sequences. (Running on oeis4.)