OFFSET
4,1
COMMENTS
The fourth column of A008305, divided by 4.
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
Vincenzo Librandi, Table of n, a(n) for n = 4..1000
N. S. Mendelsohn, Permutations with confined displacement, Canad. Math. Bull., 4 (1961), 29-38.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
FORMULA
a(n) = a(n-1)+a(n-2)+a(n-3)-2 (conjectured).
MAPLE
A000382:=-(-6+z+2*z**2+4*z**3+z**4)/(z-1)/(z**3+z**2+z-1); [Conjectured by Simon Plouffe in his 1992 dissertation.]
a:= n-> if n<4 then 0 elif n=4 then 6 else (Matrix([[11, 7, 4, 2]]). Matrix(4, (i, j)-> if (i=j-1) then 1 elif j=1 then [2, 0, 0, -1][i] else 0 fi)^(n-2))[1, 4] fi: seq(a(n), n=4..30); # Alois P. Heinz, Aug 26 2008
MATHEMATICA
a[n_] := Which[n<4, 0, n == 4, 6, True, {11, 7, 4, 2}.MatrixPower[Table[Which[i == j-1, 1, j == 1, {2, 0, 0, -1}[[i]], True, 0], {i, 1, 4}, {j, 1, 4}], n-2] // Last]; Table[a[n], {n, 4, 27}] (* Jean-François Alcover, Mar 12 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Mar 14 2014
STATUS
approved