cp's OEIS Frontend

A221542 T(n,k) = Number of 0..k arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

%I A221542 #6 Oct 18 2017 18:22:05
%S A221542 0,0,1,0,2,1,0,3,4,2,0,4,8,10,3,0,5,14,30,22,5,0,6,22,68,103,54,8,0,7,
%T A221542 32,130,303,364,134,13,0,8,44,222,716,1386,1276,334,21,0,9,58,350,
%U A221542 1455,4018,6311,4483,822,34,0,10,74,520,2658,9665,22466,28762,15740,2014,55,0,11
%N A221542 T(n,k) = Number of 0..k arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.
%C A221542 Table starts
%C A221542 ..0.....0......0........0.........0.........0..........0...........0
%C A221542 ..1.....2......3........4.........5.........6..........7...........8
%C A221542 ..1.....4......8.......14........22........32.........44..........58
%C A221542 ..2....10.....30.......68.......130.......222........350.........520
%C A221542 ..3....22....103......303.......716......1455.......2658........4487
%C A221542 ..5....54....364.....1386......4018......9665......20386.......39007
%C A221542 ..8...134...1276.....6311.....22466.....64047.....156098......338711
%C A221542 .13...334...4483....28762....125701....424593....1195561.....2941622
%C A221542 .21...822..15740...131012....703193...2814515....9156379....25546512
%C A221542 .34..2014..55274...596784...3933916..18656979...70126074...221859676
%C A221542 .55..4934.194095..2718469..22007609.123673887..537074685..1926747595
%C A221542 .89.12110.681576.12383368.123117952.819813575.4113296146.16732904887
%H A221542 R. H. Hardin, <a href="/A221542/b221542.txt">Table of n, a(n) for n = 1..2080</a>
%F A221542 Empirical for column k:
%F A221542 k=1: a(n) = a(n-1) +a(n-2)
%F A221542 k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-4)
%F A221542 k=3: a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +a(n-4)
%F A221542 k=4: a(n) = 5*a(n-1) -3*a(n-2) +a(n-3) +15*a(n-4) +3*a(n-5) for n>6
%F A221542 k=5: a(n) = 5*a(n-1) +3*a(n-2) +9*a(n-4) +6*a(n-5) +3*a(n-6)
%F A221542 k=6: a(n) = 7*a(n-1) -4*a(n-2) +6*a(n-3) +26*a(n-4) +10*a(n-5) +16*a(n-6) +12*a(n-8)
%F A221542 k=7: a(n) = 7*a(n-1) +4*a(n-2) +5*a(n-3) +20*a(n-4) +20*a(n-5) +23*a(n-6) -6*a(n-7) +3*a(n-8)
%F A221542 Empirical for row n:
%F A221542 n=2: a(n) = 1*n for n>1
%F A221542 n=3: a(n) = 1*n^2 - 1*n + 2 for n>1
%F A221542 n=4: a(n) = 1*n^3 + 1*n
%F A221542 n=5: a(n) = 1*n^4 + 1*n^3 - 3*n^2 + 10*n - 9 for n>3
%F A221542 n=6: a(n) = 1*n^5 + 2*n^4 - 6*n^3 + 21*n^2 - 31*n + 23 for n>4
%F A221542 n=7: a(n) = 1*n^6 + 3*n^5 - 8*n^4 + 25*n^3 - 30*n^2 + 20*n - 9 for n>3
%e A221542 Some solutions for n=6 k=4
%e A221542 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A221542 ..4....2....2....3....2....0....4....0....4....4....3....4....0....4....4....4
%e A221542 ..0....4....4....4....0....2....3....2....3....0....0....4....2....1....4....4
%e A221542 ..0....0....0....4....4....4....1....3....1....4....2....2....0....1....2....0
%e A221542 ..3....2....4....4....4....0....0....3....1....1....4....4....4....2....0....0
%e A221542 ..0....2....1....2....0....2....2....3....3....1....4....2....0....0....0....3
%Y A221542 Column 1 is A000045(n-1).
%Y A221542 Row 2 is A000027.
%Y A221542 Row 3 is A003682.
%Y A221542 Row 4 is A034262.
%K A221542 nonn,tabl
%O A221542 1,5
%A A221542 _R. H. Hardin_, Jan 19 2013