A000803 a(n+3) = a(n+2) + a(n+1) + a(n) - 4. (Formerly M4472 N2232)

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

T. D. Noe, Table of n, a(n) for n = 0..400

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.

Index entries for linear recurrences with constant coefficients, signature (2,0,0,-1).

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

Cf. A000804, A000805, A004306.

Sequence in context: A336065 A124012 A335354 * A198063 A323736 A093208

Adjacent sequences: A000800 A000801 A000802 * A000804 A000805 A000806

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

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

Status

approved