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A000803
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a(n+3)=a(n+2)+a(n+1)+a(n)-4.
(Formerly M4472 N2232)
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3
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0, 0, 8, 4, 8, 16, 24, 44, 80, 144, 264, 484, 888, 1632, 3000, 5516, 10144, 18656, 34312, 63108, 116072, 213488, 392664, 722220, 1328368, 2443248, 4493832, 8265444, 15202520, 27961792, 51429752, 94594060, 173985600, 320009408
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OFFSET
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0,3
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COMMENTS
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This sequence and A004306 coincide from the term "24" onwards. This follows easily by studying the two g.f.'s. - R. J. Mathar and A. Plewe, Dec 04 2007
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REFERENCES
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H. Beker and C. Mitchell, Permutations with restricted displacement, SIAM J. Algebraic Discr. Methods, 8 (1987), 338-363.
N. Metropolis et al., Permanents of cyclic (0,1) matrices, J. Combin. Theory, 7 (1969), 291-321.
H. Minc, Permanents of (0,1)-circulants, Canad. Math. Bull., 7 (1964), 253-263.
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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T. D. Noe, Table of n, a(n) for n = 0..400
Index to sequences with linear recurrences with constant coefficients, signature (2,0,0,-1).
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FORMULA
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G.f. = -4x^2*(3x-2) /((x-1)(x^3+x^2+x-1)) = 2(-5x^2+1)/(x^3+x^2+x-1)-2/(x-1) . - R. J. Mathar, Dec 04 2007
a(0)=0, a(1)=0, a(2)=8, a(3)=4, a(n)=2*a(n-1)-a(n-4). - Harvey P. Dale, Mar 25 2013
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MATHEMATICA
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LinearRecurrence[{2, 0, 0, -1}, {0, 0, 8, 4}, 40] (* Harvey P. Dale, Mar 25 2013 *)
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PROG
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(Haskell)
a000803 n = a000803_list !! n
a000803_list = 0 : 0 : 8 : zipWith (+)
(tail $ zipWith (+) (tail a000803_list) a000803_list)
(map (subtract 4) a000803_list)
-- Reinhard Zumkeller, Nov 18 2011
(PARI) concat([0, 0], Vec((8-12*x)/(1-2*x+x^4)+O(x^97))) \\ Charles R Greathouse IV, Nov 18 2011
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CROSSREFS
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Cf. A000804, A000805, A004306.
Sequence in context: A087015 A200224 A124012 * A198063 A093208 A155064
Adjacent sequences: A000800 A000801 A000802 * A000804 A000805 A000806
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KEYWORD
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nonn,easy,nice,changed
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Mar 17 2000
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STATUS
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approved
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