A228464 - OEIS

%I #23 Mar 17 2018 05:45:51

%S 44,383,1821,6254,17487,42386,92430,185727,349558,623513,1063283,

%T 1745172,2771393,4276212,6433004,9462285,13640784,19311619,26895641,

%U 36904010,49952067,66774566,88242330,115380395,149387706,191658429,243804943

%N Number of arrays of maxima of three adjacent elements of some 0..n array of length 9.

%C See A228461 for explanation of definition.

%H R. H. Hardin, <a href="/A228464/b228464.txt">Table of n, a(n) for n = 1..210</a>

%F 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.

%F Conjectures from _Colin Barker_, Mar 16 2018: (Start)

%F 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.

%F 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.

%F (End)

%e Some solutions for n=4:

%e   3   0   3   4   4   3   3   4   3   4   2   3   2   0   3   2

%e   3   0   2   4   4   0   0   2   1   3   4   3   0   0   4   0

%e   0   0   2   4   0   2   0   2   4   4   4   3   4   0   4   2

%e   0   0   1   3   1   3   1   2   4   4   4   3   4   4   4   2

%e   0   0   3   1   1   3   2   2   4   4   0   1   4   4   0   2

%e   1   0   3   0   4   4   3   2   4   4   0   1   0   4   3   2

%e   1   3   4   3   4   4   3   1   0   2   1   2   0   3   3   0

%Y Row 7 of A228461. Cf. A217949.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 22 2013