cp's OEIS Frontend

A222838 T(n,k)=Number of nXk 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.

%I A222838 #6 Jul 23 2025 03:08:11
%S A222838 1,2,2,3,7,3,7,24,24,7,19,96,72,96,19,55,384,216,216,384,55,163,1536,
%T A222838 648,600,648,1536,163,487,6144,1944,1536,1536,1944,6144,487,1459,
%U A222838 24576,5832,4056,4032,4056,5832,24576,1459,4375,98304,17496,10584,9600,9600,10584
%N A222838 T(n,k)=Number of nXk 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.
%C A222838 Table starts
%C A222838 .....1.......2.......3.......7......19......55.....163......487.....1459
%C A222838 .....2.......7......24......96.....384....1536....6144....24576....98304
%C A222838 .....3......24......72.....216.....648....1944....5832....17496....52488
%C A222838 .....7......96.....216.....600....1536....4056...10584....27744....72600
%C A222838 ....19.....384.....648....1536....4032....9600...22848....55296...133824
%C A222838 ....55....1536....1944....4056....9600...24576...55296...124416...279936
%C A222838 ...163....6144....5832...10584...22848...55296..138240...301056...642048
%C A222838 ...487...24576...17496...27744...55296..124416..301056...743424..1572864
%C A222838 ..1459...98304...52488...72600..133824..279936..642048..1572864..3833856
%C A222838 ..4375..393216..157464..190104..322944..645504.1382400..3250176..7962624
%C A222838 .13123.1572864..472392..497664..779328.1476096.3022848..6690816.15925248
%C A222838 .39367.6291456.1417176.1302936.1881600.3393024.6690816.14155776.31850496
%H A222838 R. H. Hardin, <a href="/A222838/b222838.txt">Table of n, a(n) for n = 1..312</a>
%F A222838 Empirical for column k:
%F A222838 k=1: a(n) = 4*a(n-1) -3*a(n-2) for n>4
%F A222838 k=2: a(n) = 4*a(n-1) for n>3
%F A222838 k=3: a(n) = 3*a(n-1) for n>2
%F A222838 k=4: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3) for n>4
%F A222838 k=5: a(n) = 2*a(n-1) +2*a(n-3) +a(n-4) for n>7
%F A222838 k=6: a(n) = 2*a(n-1) +2*a(n-2) -4*a(n-3) +4*a(n-4) -4*a(n-5) +2*a(n-6) -6*a(n-7) +a(n-10) for n>14
%F A222838 k=7: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) +4*a(n-5) +a(n-6) -a(n-9) for n>14
%e A222838 Some solutions for n=4 k=4
%e A222838 ..0..0..1..2....0..1..2..3....0..0..1..2....0..0..1..2....0..1..1..2
%e A222838 ..2..2..1..0....2..3..0..0....1..3..3..0....2..3..3..2....2..2..0..3
%e A222838 ..1..3..3..0....2..3..1..1....1..2..2..0....1..1..0..0....1..3..0..1
%e A222838 ..1..0..2..2....1..0..2..2....0..0..1..3....0..2..2..3....0..3..2..2
%Y A222838 Column 1 is A052919(n-2)
%K A222838 nonn,tabl
%O A222838 1,2
%A A222838 _R. H. Hardin_ Mar 06 2013