A201042 T(n,k)=Number of -k..k arrays of n elements with adjacent element differences also in -k..k

3, 5, 7, 7, 19, 17, 9, 37, 75, 41, 11, 61, 203, 295, 99, 13, 91, 429, 1111, 1161, 239, 15, 127, 781, 3011, 6083, 4569, 577, 17, 169, 1287, 6691, 21141, 33305, 17981, 1393, 19, 217, 1975, 13021, 57343, 148433, 182349, 70763, 3363, 21, 271, 2873, 23045, 131781

Offset

1,1

Comments

Table starts

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

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

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

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

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

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

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

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

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

.8119.1095951.29928491.360709449.2650872719.13991301963.58267877227

Links

R. H. Hardin, Table of n, a(n) for n = 1..9999

Formula

Empirical for columns:

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

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

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

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

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)

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)

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)

Empirical for rows:

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

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

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

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

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

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

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

Example

Some solutions for n=4 k=7
.-5...-1....2....2...-3....4...-4....4....5....2...-6...-1....1....4....2....0
.-3....0....3....1....2....4...-3....4....2...-5....1....6....5....7....4....0
.-5...-5...-4...-3....2...-2....1....5....7...-7....0....2....4....1....1....2
.-7...-1....2...-6....1...-1...-5....7....0...-1...-5....6...-3....5...-1....2

Crossrefs

Column 1 is A001333(n+1)

Column 2 is A126392

Column 3 is A126475

Column 4 is A126504

Column 5 is A126532

Row 1 is A004273(n+1)

Row 2 is A003215

Row 3 is A063494(n+1)

Sequence in context: A202664 A202124 A201088 * A142340 A185168 A131979

Adjacent sequences: A201039 A201040 A201041 * A201043 A201044 A201045

Keyword

nonn,tabl

Author

R. H. Hardin Nov 26 2011

Status

approved