A267230 Number of length-n 0..6 arrays with no following elements greater than or equal to the first repeated value.
7, 49, 315, 1981, 12327, 76237, 469623, 2884909, 17686215, 108259885, 661872471, 4042575277, 24671450343, 150466937773, 917151735159, 5587651325485, 34027698639111, 207144227712301, 1260572274312087, 7668877406965933
Offset: 1
Keywords
Examples
Some solutions for n=6: 3 2 1 3 1 2 2 0 4 0 2 0 1 3 6 3 6 6 0 6 2 3 3 3 5 2 4 1 5 4 5 6 2 1 3 1 0 5 5 2 2 6 3 0 3 1 5 4 5 3 6 3 4 6 2 5 4 4 1 4 0 4 2 2 2 1 1 4 1 5 0 1 5 0 6 6 3 2 4 0 3 0 6 0 1 2 4 1 2 0 6 6 1 4 0 6
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A267232.
Formula
Empirical: a(n) = 27*a(n-1) - 301*a(n-2) + 1785*a(n-3) - 6034*a(n-4) + 11508*a(n-5) - 11304*a(n-6) + 4320*a(n-7) for n > 8.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(7 - 140*x + 1099*x^2 - 4270*x^3 + 8428*x^4 - 7476*x^5 + 1512*x^6 + 720*x^7) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)^2).
a(n) = (-45*2^n - 40*3^n - 45*4^n - 72*5^n + 557*6^n + 5*2^(1 + n)*3^n*n - 72) / 360 for n>1.
(End)
Comments