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A189604
Number of n X 3 array permutations with each element not moving, or moving one space E, S or NW.
1
1, 6, 20, 72, 256, 912, 3248, 11568, 41200, 146736, 522608, 1861296, 6629104, 23609904, 84087920, 299483568, 1066626544, 3798846768, 13529793392, 48187073712, 171620807920, 611236571184, 2176951329392, 7753327130544
OFFSET
1,2
COMMENTS
Column 3 of A189610.
Binomial transform of A006131 starting (1, 5, 9, 29, 65, ...). - Gary W. Adamson, Feb 19 2014
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) + 2*a(n-2).
G.f.: (x+3*x^2)/(1-3*x-2*x^2). - Vladimir Kruchinin, May 13 2011
EXAMPLE
Some solutions for 4 X 3:
.
4 5 1 0 5 1 0 1 2 0 1 2
0 3 2 7 4 2 3 4 5 3 4 5
6 7 8 3 6 8 6 11 8 10 7 8
9 10 11 9 10 11 9 7 10 6 9 11
.
4 0 1 0 1 2 4 1 2
7 3 2 3 8 5 0 3 5
10 11 5 6 4 7 6 7 8
6 9 8 9 10 11 9 10 11
MATHEMATICA
a[n_] := Sum[Sum[4^j Binomial[k-j+1, j], {j, 0, Quotient[k+1, 2]}]* Binomial[n-1, k], {k, 0, n-1}];
a /@ Range[1, 24] (* Jean-François Alcover, Sep 24 2019, after Gary W. Adamson *)
CROSSREFS
Cf. A006131.
Sequence in context: A075055 A146891 A235367 * A153372 A028402 A092760
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 24 2011
STATUS
approved