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A058937
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Maximal exponent of x in all terms of Somos polynomial of order n.
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4
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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
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OFFSET
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1,7
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COMMENTS
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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
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009
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STATUS
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approved
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