A201042 - OEIS

%I #5 Mar 31 2012 12:36:42

%S 3,5,7,7,19,17,9,37,75,41,11,61,203,295,99,13,91,429,1111,1161,239,15,

%T 127,781,3011,6083,4569,577,17,169,1287,6691,21141,33305,17981,1393,

%U 19,217,1975,13021,57343,148433,182349,70763,3363,21,271,2873,23045,131781

%N T(n,k)=Number of -k..k arrays of n elements with adjacent element differences also in -k..k

%C Table starts

%C ....3.......5........7.........9.........11..........13..........15

%C ....7......19.......37........61.........91.........127.........169

%C ...17......75......203.......429........781........1287........1975

%C ...41.....295.....1111......3011.......6691.......13021.......23045

%C ...99....1161.....6083.....21141......57343......131781......268983

%C ..239....4569....33305....148433.....491429.....1333683.....3139529

%C ..577...17981...182349...1042167....4211559....13497523....36644243

%C .1393...70763...998383...7317185...36093157...136601483...427707523

%C .3363..278483..5466269..51374875..309319197..1382473365..4992154799

%C .8119.1095951.29928491.360709449.2650872719.13991301963.58267877227

%H R. H. Hardin, <a href="/A201042/b201042.txt">Table of n, a(n) for n = 1..9999</a>

%F Empirical for columns:

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

%F k=2: a(n) = 4*a(n-1) -a(n-3)

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

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

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

%F k=6: a(n) = 10*a(n-1) +3*a(n-2) -18*a(n-3) -a(n-4) +8*a(n-5) -a(n-7)

%F k=7: a(n) = 11*a(n-1) +10*a(n-2) -24*a(n-3) -15*a(n-4) +13*a(n-5) +7*a(n-6) -2*a(n-7) -a(n-8)

%F Empirical for rows:

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

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

%F n=3: a(k) = (14/3)*k^3 + 7*k^2 + (13/3)*k + 1

%F n=4: a(k) = (29/4)*k^4 + (29/2)*k^3 + (51/4)*k^2 + (11/2)*k + 1

%F n=5: a(k) = (169/15)*k^5 + (169/6)*k^4 + 32*k^3 + (119/6)*k^2 + (101/15)*k + 1

%F n=6: a(k) = (2101/120)*k^6 + (2101/40)*k^5 + (1753/24)*k^4 + (1405/24)*k^3 + (569/20)*k^2 + (119/15)*k + 1

%F n=7: a(k) = (17141/630)*k^7 + (17141/180)*k^6 + (28177/180)*k^5 + (2759/18)*k^4 + (17299/180)*k^3 + (6929/180)*k^2 + (1921/210)*k + 1

%e Some solutions for n=4 k=7

%e .-5...-1....2....2...-3....4...-4....4....5....2...-6...-1....1....4....2....0

%e .-3....0....3....1....2....4...-3....4....2...-5....1....6....5....7....4....0

%e .-5...-5...-4...-3....2...-2....1....5....7...-7....0....2....4....1....1....2

%e .-7...-1....2...-6....1...-1...-5....7....0...-1...-5....6...-3....5...-1....2

%Y Column 1 is A001333(n+1)

%Y Column 2 is A126392

%Y Column 3 is A126475

%Y Column 4 is A126504

%Y Column 5 is A126532

%Y Row 1 is A004273(n+1)

%Y Row 2 is A003215

%Y Row 3 is A063494(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Nov 26 2011