

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
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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

Nathaniel Johnston, Table of n, a(n) for n = 0..100
Torleiv Kløve, Spheres of Permutations under the Infinity Norm  Permutations with limited displacement. Reports in Informatics, Department of Informatics, University of Bergen, Norway, no. 376, November 2008.


FORMULA

a(n) = A002526(n1) + A002528(n1) + A188494(n1).  Nathaniel Johnston, Apr 08 2011
G.f.: x*(x^3+x^21)*(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=j1, 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 == j1, 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}] (* JeanFrançois Alcover, Mar 17 2014, after Alois P. Heinz *)


CROSSREFS

Sequence in context: A297708 A284701 A011455 * A295974 A324365 A192764
Adjacent sequences: A188488 A188489 A188490 * A188492 A188493 A188494


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 01 2011


EXTENSIONS

Name and comments edited by Nathaniel Johnston, Apr 08 2011


STATUS

approved



