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A137360
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a(n) = Sum_{k <= n/2 } k*binomial(n-2k, 3k+1).
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4
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0, 0, 0, 0, 0, 0, 1, 5, 15, 35, 70, 128, 226, 402, 735, 1375, 2588, 4830, 8882, 16108, 28943, 51785, 92573, 165525, 295869, 528069, 940259, 1669725, 2957941, 5229953, 9233748, 16284106, 28688451, 50490125, 88765885, 155891305, 273495479, 479360847, 839451764
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OFFSET
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0,8
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 8, -7, 6, -2, 0, -1).
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FORMULA
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G.f.: x^6*(1-x)/(x^5+x^3-3*x^2+3*x-1)^2. - Alois P. Heinz, Oct 23 2008
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MAPLE
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a:= n-> (Matrix([[35, 15, 5, 1, 0$6]]). Matrix (10, (i, j)-> if i=j-1 then 1 elif j=1 then [6, -15, 20, -15, 8, -7, 6, -2, 0, -1][i] else 0 fi)^n)[1, 10]: seq (a(n), n=0..50); # Alois P. Heinz, Oct 23 2008
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MATHEMATICA
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Table[Sum[k Binomial[n-2k, 3k+1], {k, n/2}], {n, 0, 40}] (* or *) LinearRecurrence[ {6, -15, 20, -15, 8, -7, 6, -2, 0, -1}, {0, 0, 0, 0, 0, 0, 1, 5, 15, 35}, 40] (* Harvey P. Dale, May 31 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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