|
%I #20 Feb 08 2022 22:26:16
%S 1,6,20,72,256,912,3248,11568,41200,146736,522608,1861296,6629104,
%T 23609904,84087920,299483568,1066626544,3798846768,13529793392,
%U 48187073712,171620807920,611236571184,2176951329392,7753327130544
%N Number of n X 3 array permutations with each element not moving, or moving one space E, S or NW.
%C Column 3 of A189610.
%C Binomial transform of A006131 starting (1, 5, 9, 29, 65, ...). - _Gary W. Adamson_, Feb 19 2014
%H R. H. Hardin, <a href="/A189604/b189604.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 3*a(n-1) + 2*a(n-2).
%F G.f.: (x+3*x^2)/(1-3*x-2*x^2). - _Vladimir Kruchinin_, May 13 2011
%e Some solutions for 4 X 3:
%e .
%e 4 5 1 0 5 1 0 1 2 0 1 2
%e 0 3 2 7 4 2 3 4 5 3 4 5
%e 6 7 8 3 6 8 6 11 8 10 7 8
%e 9 10 11 9 10 11 9 7 10 6 9 11
%e .
%e 4 0 1 0 1 2 4 1 2
%e 7 3 2 3 8 5 0 3 5
%e 10 11 5 6 4 7 6 7 8
%e 6 9 8 9 10 11 9 10 11
%t 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}];
%t a /@ Range[1, 24] (* _Jean-François Alcover_, Sep 24 2019, after _Gary W. Adamson_ *)
%Y Cf. A006131.
%K nonn
%O 1,2
%A _R. H. Hardin_, Apr 24 2011
|
