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A000803
a(n+3) = a(n+2) + a(n+1) + a(n) - 4.
(Formerly M4472 N2232)
3
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
OFFSET
0,3
COMMENTS
This sequence and A004306 coincide from the term "24" onwards. This follows easily by studying the two g.f.'s. - R. J. Mathar and Andrew S. Plewe, Dec 04 2007
REFERENCES
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
Henry Beker and Chris Mitchell, Permutations with restricted displacement, SIAM J. Algebraic Discrete Methods 8 (1987), no. 3, 338--363. MR0897734 (89f:05009).
N. Metropolis, M. L. Stein, P. R. Stein, 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.
FORMULA
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
MATHEMATICA
LinearRecurrence[{2, 0, 0, -1}, {0, 0, 8, 4}, 40] (* Harvey P. Dale, Mar 25 2013 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy,nice
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Mar 17 2000
STATUS
approved