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A267230
Number of length-n 0..6 arrays with no following elements greater than or equal to the first repeated value.
1
7, 49, 315, 1981, 12327, 76237, 469623, 2884909, 17686215, 108259885, 661872471, 4042575277, 24671450343, 150466937773, 917151735159, 5587651325485, 34027698639111, 207144227712301, 1260572274312087, 7668877406965933
OFFSET
1,1
COMMENTS
Column 6 of A267232.
LINKS
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)
EXAMPLE
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
CROSSREFS
Cf. A267232.
Sequence in context: A357146 A133046 A200783 * A188868 A267469 A126639
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 12 2016
STATUS
approved