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A264257 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change 0,1 0,-1 0,2 1,0 or -1,0. 12

%I #6 Nov 10 2015 12:00:47

%S 4,10,9,29,33,25,89,157,180,64,260,1124,1920,760,169,772,5468,23805,

%T 14893,3653,441,2281,32361,254393,397462,147797,16401,1156,6741,

%U 181644,2896729,7877184,7467925,1273553,76330,3025,19940,1005279,32417000

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

%C Table starts

%C .....4......10.........29.............89.............260..............772

%C .....9......33........157...........1124............5468............32361

%C ....25.....180.......1920..........23805..........254393..........2896729

%C ....64.....760......14893.........397462.........7877184........180566464

%C ...169....3653.....147797........7467925.......301623757......13509166173

%C ...441...16401....1273553......132080760.....10265640512.....917543249651

%C ..1156...76330...11868873.....2411543681....372797128908...65622177560404

%C ..3025..348480..105792288....43298007242..13053476555570.4563171069771635

%C ..7921.1607429..966768105...784323747917.466441716294953

%C .20736.7373520.8711282401.14141096261412

%H R. H. Hardin, <a href="/A264257/b264257.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)

%F k=2: a(n) = a(n-1) +16*a(n-2) +9*a(n-3) -29*a(n-4) -9*a(n-5) +16*a(n-6) -a(n-7) -a(n-8)

%F k=3: [order 33]

%F Empirical for row n:

%F n=1: a(n) = 2*a(n-1) +2*a(n-2) +2*a(n-3) +4*a(n-5) -a(n-8)

%F n=2: [order 47]

%e Some solutions for n=3 k=4

%e ..1..0..7..8..3....5..6..1..4..2....5..2..3..4..9....5..2..0..1..3

%e .10.11..2..6..4....0..7..8..3.14....0..1..8.13..7....6.11.12..7..4

%e ..5.12.13.14..9...11.16.13.12..9...15..6.17.18.19...15.16.13..8..9

%e .16.17.15.19.18...10.15.18.19.17...10.11.12.16.14...10.17.18.19.14

%Y Column 1 is A007598(n+2).

%Y Row 1 is A264158.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 09 2015

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Last modified May 18 12:18 EDT 2024. Contains 372630 sequences. (Running on oeis4.)