A222002 - OEIS

%I #9 Aug 14 2018 21:03:28

%S 24,157,704,2470,7328,19228,45894,101543,211070,416275,784864,1423138,

%T 2493494,4238102,7010394,11316307,17867564,27649657,42007616,62753110,

%U 92296932,133811472,191428382,270477287,377772098,521952239,713886912

%N Number of n X 4 arrays with each row a permutation of 1..4 having at least as many downsteps as the preceding row, with rows in lexicographically nonincreasing order.

%C Column 4 of A222005.

%H R. H. Hardin, <a href="/A222002/b222002.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).

%F Empirical g.f.: x*(24 - 107*x + 297*x^2 - 599*x^3 + 893*x^4 - 968*x^5 + 750*x^6 - 405*x^7 + 145*x^8 - 31*x^9 + 3*x^10) / (1 - x)^11. - _Colin Barker_, Aug 14 2018

%e Some solutions for n=3:

%e ..2..1..3..4....2..3..1..4....4..1..2..3....3..2..1..4....4..1..3..2

%e ..1..4..2..3....2..1..3..4....2..4..1..3....3..2..1..4....3..2..4..1

%e ..1..3..2..4....1..4..2..3....2..3..1..4....3..1..4..2....2..1..4..3

%Y Cf. A222005.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 03 2013