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

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

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).

Crossrefs

Cf. A000804, A000805, A004306.

Programs

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

Mathematica

LinearRecurrence[{2,0,0,-1},{0,0,8,4},40] (* Harvey P. Dale, Mar 25 2013 *)

PARI

concat([0,0],Vec((8-12*x)/(1-2*x+x^4)+O(x^97))) \\ Charles R Greathouse IV, Nov 18 2011

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

Extensions

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