A126504 -id:A126504 - cp's OEIS frontend

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

R. H. Hardin Nov 26 2011

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

			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

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

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)

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

A126530 Number of base 9 n-digit numbers with adjacent digits differing by five or less.

Original entry on oeis.org

1, 9, 69, 541, 4231, 33101, 258953, 2025831, 15848391, 123984439, 969949627, 7588067405, 59362636295, 464403174075, 3633098554089, 28422297349753, 222352070721709, 1739494972761653, 13608340819322255, 106460175369651261

Offset: 0

R. H. Hardin, Dec 28 2006

[Empirical] a(base,n)=a(base-1,n)+11^(n-1) for base>=5n-4; a(base,n)=a(base-1,n)+11^(n-1)-2 when base=5n-5.

Cf. Base 9 differing by four or less A126504, three or less A126477, two or less A126396, one or less A126363.

Conjectures from Colin Barker, Jun 01 2017: (Start)
G.f.: (1 + 2*x - x^2 - x^3) / ((1 + x)*(1 - 8*x + x^2 + 3*x^3)).
a(n) = 7*a(n-1) + 7*a(n-2) - 4*a(n-3) - 3*a(n-4) for n>3.
(End)

cp's OEIS Frontend

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

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