|
|
A188491
|
|
Number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i, p(1) <= 3, and p(4) >= 2.
|
|
7
|
|
|
0, 1, 2, 6, 14, 48, 152, 476, 1425, 4340, 13288, 40852, 125124, 382888, 1171612, 3587505, 10985790, 33638142, 102988410, 315318756, 965432832, 2955964296, 9050522241, 27710613432, 84843476928, 259771465608, 795361704776, 2435217884992
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
a(n) is also the permanent of the n X n matrix that has ones on its diagonal, ones on its three superdiagonals (with the exception of a single zero in the (1,4)-entry), ones on its three subdiagonals (with the exception of a single zero in the (4,1)-entry), and is zero elsewhere.
This is row 5 of Kløve's Table 3.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: -x*(x^3+x^2-1)*(x^3+2*x^2+x+1) / (x^13 +3*x^12 +3*x^11 +5*x^10 +9*x^9 +7*x^8 -3*x^7 -19*x^6 -21*x^5 -13*x^4 -3*x^3 -3*x^2 -x+1).
|
|
MAPLE
|
a:= n-> (Matrix(13, (i, j)-> `if`(i=j-1, 1, `if`(i=13, [-1, -3, -3, -5, -9, -7, 3, 19, 21, 13, 3, 3, 1][j], 0)))^n. <<0, 0, 1, (0$6), 1, 2, 6, 14>>)[9, 1]: seq(a(n), n=0..30); # Alois P. Heinz, Apr 08 2011
|
|
MATHEMATICA
|
a[n_] := ((Table[Which[i == j-1, 1, i == 13, {-1, -3, -3, -5, -9, -7, 3, 19, 21, 13, 3, 3, 1}[[j]], True, 0], {i, 1, 13}, {j, 1, 13}] // MatrixPower[#, n]&).{0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 6, 14})[[9]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 17 2014, after Alois P. Heinz *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|