A246737 T(n,k)=Number of length n+4 0..k arrays with no pair in any consecutive five terms totalling exactly k.

2, 12, 2, 124, 16, 2, 424, 260, 22, 2, 1566, 1096, 548, 30, 2, 3876, 5430, 2884, 1156, 40, 2, 9368, 15960, 18966, 7612, 2436, 52, 2, 18768, 47432, 66378, 66294, 19992, 5132, 68, 2, 36250, 109552, 241544, 276762, 231414, 52112, 10812, 90, 2, 63100, 246890

Offset

1,1

Comments

Table starts

.2..12....124.....424......1566.......3876........9368........18768

.2..16....260....1096......5430......15960.......47432.......109552

.2..22....548....2884.....18966......66378......241544.......643048

.2..30...1156....7612.....66294.....276762.....1231304......3780600

.2..40...2436...19992....231414....1152576.....6272072.....22219408

.2..52...5132...52112....807630....4791012....31944440....130526848

.2..68..10812..135776...2818830...19906740...162700376....766650656

.2..90..22780..354428...9838974...82727094...828690200...4502888280

.2.120..47996..926912..34342350..343911336..4220813912..26449024896

.2.160.101124.2426008.119869158.1430080296.21498069128.155366381200

Links

R. H. Hardin, Table of n, a(n) for n = 1..1661

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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

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

k=4: [order 16]

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

k=6: [order 23]

k=7: a(n) = 4*a(n-1) +4*a(n-2) +4*a(n-3) +18*a(n-4) +12*a(n-5) -4*a(n-7) -a(n-8)

k=8: [order 24]

k=9: a(n) = 6*a(n-1) +4*a(n-2) +6*a(n-3) +38*a(n-4) +18*a(n-5) -6*a(n-7) -a(n-8)

Empirical for row n:

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

n=2: [order 11]

n=3: [order 13]

n=4: [order 15]

n=5: [order 17]

n=6: [order 19]

n=7: [order 21]

Example

Some solutions for n=4 k=4
..3....4....3....1....1....0....2....1....1....0....2....3....2....4....0....0
..3....1....2....4....4....1....0....4....1....0....4....4....4....3....2....0
..3....1....3....1....2....2....1....2....2....1....3....2....1....4....0....0
..4....1....4....4....1....1....1....1....4....0....3....3....4....4....0....0
..4....4....4....1....4....0....0....1....4....0....3....4....4....4....1....0
..4....1....4....1....1....0....0....1....1....2....3....3....1....3....0....2
..3....2....2....2....4....1....2....0....1....0....4....3....1....3....2....1
..4....4....1....1....1....1....0....2....2....1....3....4....2....3....0....0

Crossrefs

Column 2 is A174469(n+18)

Sequence in context: A222804 A128268 A185633 * A012626 A012629 A371589

Adjacent sequences: A246734 A246735 A246736 * A246738 A246739 A246740

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 02 2014

Status

approved