|
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
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 A. Plewe, Dec 04 2007
|
|
|
REFERENCES
| 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).
|
|
|
LINKS
| 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).
|
|
|
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
|
|
|
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: A087015 A200224 A124012 * A198063 A093208 A155064
Adjacent sequences: A000800 A000801 A000802 * A000804 A000805 A000806
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Mar 17 2000
|
| |
|
|
