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 A001634 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) 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES 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). LINKS T. D. Noe, Table of n, a(n) for n=0..500 Daniel C. Fielder, Special integer sequences controlled by three parameters, Fibonacci Quarterly 6, 1968, 64-70. Gregory T. Minton, Linear recurrence sequences satisfying congruence conditions, Proc. Amer. Math. Soc. 142 (2014), no. 7, 2337--2352. MR3195758. Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 1). FORMULA 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 MAPLE A001634:=-z*(2+3*z+4*z**2)/(1+z)/(z**3+z-1); # Simon Plouffe in his 1992 dissertation 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 MATHEMATICA LinearRecurrence[{0, 1, 1, 1}, {0, 2, 3, 6}, 100] (* Vladimir Joseph Stephan Orlovsky, Jul 01 2011 *) PROG (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)) -- Reinhard Zumkeller, Mar 23 2012 (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 */ CROSSREFS Cf. A013979, A107458. Sequence in context: A039653 A106379 A232929 * A172989 A095113 A002517 Adjacent sequences:  A001631 A001632 A001633 * A001635 A001636 A001637 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)