login
a(n+3) = a(n+2) + a(n+1) + a(n) - 4.
(Formerly M4472 N2232)
3

%I M4472 N2232 #38 Sep 24 2018 16:53:13

%S 0,0,8,4,8,16,24,44,80,144,264,484,888,1632,3000,5516,10144,18656,

%T 34312,63108,116072,213488,392664,722220,1328368,2443248,4493832,

%U 8265444,15202520,27961792,51429752,94594060,173985600,320009408

%N a(n+3) = a(n+2) + a(n+1) + a(n) - 4.

%C 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

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A000803/b000803.txt">Table of n, a(n) for n = 0..400</a>

%H Henry Beker and Chris Mitchell, <a href="http://dx.doi.org/10.1137/0608029">Permutations with restricted displacement</a>, SIAM J. Algebraic Discrete Methods 8 (1987), no. 3, 338--363. MR0897734 (89f:05009).

%H N. Metropolis, M. L. Stein, P. R. Stein, <a href="http://dx.doi.org/10.1016/S0021-9800(69)80058-X">Permanents of cyclic (0,1) matrices</a>, J. Combin. Theory, 7 (1969), 291-321.

%H H. Minc, <a href="http://dx.doi.org/10.4153/CMB-1964-023-3">Permanents of (0,1)-circulants</a>, Canad. Math. Bull., 7 (1964), 253-263.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-1).

%F 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

%F 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

%t LinearRecurrence[{2,0,0,-1},{0,0,8,4},40] (* _Harvey P. Dale_, Mar 25 2013 *)

%o (Haskell)

%o a000803 n = a000803_list !! n

%o a000803_list = 0 : 0 : 8 : zipWith (+)

%o (tail $ zipWith (+) (tail a000803_list) a000803_list)

%o (map (subtract 4) a000803_list)

%o -- _Reinhard Zumkeller_, Nov 18 2011

%o (PARI) concat([0,0],Vec((8-12*x)/(1-2*x+x^4)+O(x^97))) \\ _Charles R Greathouse IV_, Nov 18 2011

%Y Cf. A000804, A000805, A004306.

%K nonn,easy,nice

%O 0,3

%A _N. J. A. Sloane_

%E More terms from Larry Reeves (larryr(AT)acm.org), Mar 17 2000