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