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A001634
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a(n) = a(n-2) + a(n-3) + a(n-4), with initial values a(0) = 0, a(1) = 2, a(2) = 3, a(3) = 6.
(Formerly M0746 N0281)
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8
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0, 2, 3, 6, 5, 11, 14, 22, 30, 47, 66, 99, 143, 212, 308, 454, 663, 974, 1425, 2091, 3062, 4490, 6578, 9643, 14130, 20711, 30351, 44484, 65192, 95546, 140027, 205222, 300765, 440795, 646014, 946782, 1387574, 2033591, 2980370, 4367947, 6401535, 9381908
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OFFSET
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0,2
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REFERENCES
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E.-B. Escott, Reply to Query 1484, L'Intermédiaire des Mathématiciens, 8 (1901), 63-64.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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G.f.: x(2 + 3x + 4x^2)/(1 - x^2 - x^3 - x^4).
a(n) = Sum_{k=0..(n-1)/2)}(Sum_{j=0..k+1}(binomial(j,n-2*k-j-1)*binomial(k+1,j))/(k+1))*(n+1). - Vladimir Kruchinin, Mar 22 2016
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MAPLE
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a:= n-> (Matrix([[0, 4, -1, -1]]). Matrix(4, (i, j)-> if (i=j-1) then 1 elif j=1 then [0, 1, 1, 1][i] else 0 fi)^n)[1, 1]: seq(a(n), n=0..40); # Alois P. Heinz, Aug 01 2008
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MATHEMATICA
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CoefficientList[Series[x (2+3x+4x^2)/(1-x^2-x^3-x^4), {x, 0, 50}], x] (* Harvey P. Dale, Mar 26 2023 *)
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PROG
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(PARI) a(n)=if(n<0, 0, polcoeff(x*(2+3*x+4*x^2)/(1-x^2-x^3-x^4)+x*O(x^n), n))
(Haskell)
a001634 n = a001634_list !! n
a001634_list = 0 : 2 : 3 : 6 : zipWith (+) a001634_list
(zipWith (+) (tail a001634_list) (drop 2 a001634_list))
(Maxima)
a(n):=(sum(sum(binomial(j, n-2*k-j-1)*binomial(k+1, j), j, 0, k+1)/(k+1), k, 0, (n-1)/2))*(n+1); /* Vladimir Kruchinin, Mar 22 2016 */
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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