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 A058937 Maximal exponent of x in all terms of Somos polynomial of order n. 4
 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, 92, 100, 108, 117, 126, 135, 145, 155, 165, 176, 187, 198, 210, 222, 234, 247, 260, 273, 287, 301, 315, 330, 345, 360, 376, 392, 408, 425, 442, 459, 477, 495, 513, 532, 551 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS This sequence differs from A001840 only in four terms preceding it. That is, A001840(n) = a(n+5). 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 LINKS M. Somos, Somos Polynomials FORMULA a(n) = 1 + a(n-1) + a(n-3) - a(n-4) for all n in Z. 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 a(n) = a(7-n) for all n in Z. - Michael Somos, Oct 18 2018 MATHEMATICA 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}] a[ n_] := Quotient[ Binomial[n - 3, 2], 3]; (* Michael Somos, Oct 18 2018 *) PROG (Sage) [floor(binomial(n, 2)/3) for n in range(-2, 59)] # Zerinvary Lajos, Dec 01 2009 (PARI) {a(n) = binomial(n-3, 2)\3}; /* Michael Somos, Oct 18 2018 */ CROSSREFS Cf. A001840. Sequence in context: A211004 A062781 A145919 * A130518 A001840 A022794 Adjacent sequences:  A058934 A058935 A058936 * A058938 A058939 A058940 KEYWORD nonn AUTHOR Robert G. Wilson v, Jan 11 2001 EXTENSIONS G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009 STATUS approved

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Last modified November 29 02:12 EST 2020. Contains 338756 sequences. (Running on oeis4.)