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

Author

R. H. Hardin, Sep 02 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 2 is A174469(n+18)

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]