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A264272 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having index change +-(.,.) 0,0 1,0 or 1,2.

%I A264272 #6 Nov 10 2015 11:32:23
%S A264272 4,10,9,25,48,25,65,256,305,64,169,1280,3721,1800,169,442,6400,40626,
%T A264272 50625,10933,441,1156,32000,443556,1143000,707281,65856,1156,3026,
%U A264272 160000,4861800,25806400,33729146,9834496,397970,3025,7921,800000,53290000
%N A264272 T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having index change +-(.,.) 0,0 1,0 or 1,2.
%C A264272 Table starts
%C A264272 ....4......10.........25...........65.............169................442
%C A264272 ....9......48........256.........1280............6400..............32000
%C A264272 ...25.....305.......3721........40626..........443556............4861800
%C A264272 ...64....1800......50625......1143000........25806400..........600090240
%C A264272 ..169...10933.....707281.....33729146......1608491236........80568542340
%C A264272 ..441...65856....9834496....981994496.....98054154496.....10563801093680
%C A264272 .1156..397970..137007025..28735927165...6027088830169...1398071103483637
%C A264272 .3025.2402455.1908029761.839596650695.369450492999025.184549492112860840
%H A264272 R. H. Hardin, <a href="/A264272/b264272.txt">Table of n, a(n) for n = 1..127</a>
%F A264272 Empirical for column k:
%F A264272 k=1: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)
%F A264272 k=2: [order 8]
%F A264272 k=3: a(n) = 14*a(n-1) +14*a(n-2) -210*a(n-3) +210*a(n-5) -14*a(n-6) -14*a(n-7) +a(n-8)
%F A264272 k=4: [order 52]
%F A264272 k=5: [order 96]
%F A264272 Empirical for row n:
%F A264272 n=1: a(n) = 3*a(n-1) -3*a(n-3) +a(n-4)
%F A264272 n=2: a(n) = 5*a(n-1) for n>3
%F A264272 n=3: [order 22]
%F A264272 n=4: [order 25] for n>27
%e A264272 Some solutions for n=3 k=4
%e A264272 ..5..8..7..3..4....5..1..9..3..4....0..8..2..3..4....0..8..2..3..9
%e A264272 ..0..6..2..1.14....0.11..2..8.14....5.13.14..1..9....5..1.12.13..4
%e A264272 .10.18.19.13..9...10.18..7..6.19...15.16.12..6..7...15.16..7..6.19
%e A264272 .15.16.17.11.12...15.16.17.13.12...10.11.17.18.19...10.11.17.18.14
%Y A264272 Column 1 is A007598(n+2).
%Y A264272 Row 1 is A166516(n+2).
%K A264272 nonn,tabl
%O A264272 1,1
%A A264272 _R. H. Hardin_, Nov 10 2015