A267475 Number of length-7 0..n arrays with no following elements larger than the first repeated value.
71, 1112, 8770, 44901, 171601, 532840, 1418740, 3357537, 7240267, 14483216, 27233174, 48620533, 83065269, 136640848, 217501096, 336375073, 507134991, 747442216, 1079476394, 1530752741, 2135032537, 2933331864, 3975033628
Offset: 1
Keywords
Examples
Some solutions for n=5: ..3....4....0....4....5....2....5....3....2....0....5....5....1....5....0....2 ..0....0....4....4....3....0....3....4....0....1....0....0....4....3....2....3 ..1....1....1....0....4....4....0....1....5....5....4....2....3....5....0....2 ..3....4....2....0....4....2....4....0....5....0....4....4....0....4....3....1 ..4....5....3....4....1....0....1....1....4....2....2....0....5....1....5....2 ..3....0....3....1....0....4....4....5....2....3....3....1....4....4....2....4 ..4....3....3....1....0....2....2....1....2....3....4....4....3....2....1....0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A267471.
Formula
Empirical: a(n) = n^7 + (69/20)*n^6 + (17/2)*n^5 + (97/6)*n^4 + 20*n^3 + (893/60)*n^2 + 6*n + 1.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(71 + 544*x + 1862*x^2 + 1901*x^3 + 651*x^4 + 4*x^5 + 8*x^6 - x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)
Comments