A264106 - OEIS

%I #28 Jul 28 2016 21:58:38

%S 9,40,169,714,3025,12816,54289,229970,974169,4126648,17480761,

%T 74049690,313679521,1328767776,5628750625,23843770274,101003831721,

%U 427859097160,1812440220361,7677619978602,32522920134769,137769300517680

%N Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 0,2 or 1,1.

%C Column 2 of A264110.

%H R. H. Hardin, <a href="/A264106/b264106.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 4*a(n-3) + a(n-4) for n>4.

%F Empirical: a(n) = round((1/10)*(5+3*sqrt(5))*A000045(3n+3)). - _John M. Campbell_, Jul 06 2016

%F Empirical g.f.: x*(9+4*x+9*x^2+2*x^3) / ((1+x^2)*(1-4*x-x^2)). - _Colin Barker_, Jul 07 2016

%e Some solutions for n=4:

%e ..4..1..2....4..1..2....4..5..2....0..1..2....0..5..2....0..1..2....0..1..2

%e ..7..0..5....3..0..5....7..0..1....3..4..5....3..8..1....5..8..3....3..8..5

%e ..6..3..8....6..7..8...10..3..8....8.11..6....6.11..4....6.11..4....6.11..4

%e .13.10.11...11.10..9....9..6.11....9.10..7....9.10..7....9.10..7....9.14..7

%e .14..9.12...12.13.14...12.13.14...14.13.12...12.13.14...12.13.14...12.13.10

%Y Cf. A000045, A264110.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 03 2015