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
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]
Comments