cp's OEIS Frontend

A263816 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 0,1 0,2 or 1,0.

%I A263816 #8 Jun 02 2025 12:14:54
%S A263816 9,82,32,572,948,121,3682,18776,11305,450,25001,333429,643905,134028,
%T A263816 1681,170946,6425985,31916832,21876416,1590733,6272,1157993,124854432,
%U A263816 1746531193,3019386508,744805993,18875976,23409,7844192,2392853088
%N A263816 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 0,1 0,2 or 1,0.
%C A263816 Table starts
%C A263816 ......9.........82..........572...........3682...........25001.........170946
%C A263816 .....32........948........18776.........333429.........6425985......124854432
%C A263816 ....121......11305.......643905.......31916832......1746531193....96761217077
%C A263816 ....450.....134028.....21876416.....3019386508....469723808009.74221751084228
%C A263816 ...1681....1590733....744805993...286407546797.126619013196417
%C A263816 ...6272...18875976..25345430544.27150876030959
%C A263816 ..23409..223995034.862592912860
%C A263816 ..87362.2658056430
%C A263816 .326041
%H A263816 R. H. Hardin, <a href="/A263816/b263816.txt">Table of n, a(n) for n = 1..49</a>
%F A263816 Empirical for column k:
%F A263816 k=1: a(n) = 3*a(n-1) +3*a(n-2) -a(n-3)
%F A263816 k=2: a(n) = 10*a(n-1) +23*a(n-2) -10*a(n-3) -a(n-4)
%F A263816 k=3: [order 15]
%F A263816 k=4: [order 82]
%F A263816 Empirical for row n:
%F A263816 n=1: [linear recurrence of order 26]
%e A263816 Some solutions for n=2 k=4
%e A263816 ..0..1..3..2..4....0..3..2..8..4....0..6..2..8..4....0..3..2..8..4
%e A263816 ..5..6..7..8..9....6..1.12..9..7....7..1..9..3.14....5..1..9..6..7
%e A263816 .12.10.11.14.13....5.10.13.11.14....5.11.10.13.12...12.10.11.14.13
%Y A263816 Column 1 is A006253(n+1).
%K A263816 nonn,tabl
%O A263816 1,1
%A A263816 _R. H. Hardin_, Oct 27 2015