A228464 Number of arrays of maxima of three adjacent elements of some 0..n array of length 9.
44, 383, 1821, 6254, 17487, 42386, 92430, 185727, 349558, 623513, 1063283, 1745172, 2771393, 4276212, 6433004, 9462285, 13640784, 19311619, 26895641, 36904010, 49952067, 66774566, 88242330, 115380395, 149387706, 191658429, 243804943
Offset: 1
Keywords
Examples
Some solutions for n=4: 3 0 3 4 4 3 3 4 3 4 2 3 2 0 3 2 3 0 2 4 4 0 0 2 1 3 4 3 0 0 4 0 0 0 2 4 0 2 0 2 4 4 4 3 4 0 4 2 0 0 1 3 1 3 1 2 4 4 4 3 4 4 4 2 0 0 3 1 1 3 2 2 4 4 0 1 4 4 0 2 1 0 3 0 4 4 3 2 4 4 0 1 0 4 3 2 1 3 4 3 4 4 3 1 0 2 1 2 0 3 3 0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = (4/315)*n^7 + (1/5)*n^6 + (91/45)*n^5 + (63/8)*n^4 + (2557/180)*n^3 + (517/40)*n^2 + (2419/420)*n + 1 = (n+1) *(n+2) *(32*n^5 + 408*n^4 + 3808*n^3 + 7605*n^2 + 5367*n + 1260)/2520.
Conjectures from Colin Barker, Mar 16 2018: (Start)
G.f.: x*(44 + 31*x - 11*x^2 - 54*x^3 + 75*x^4 - 28*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