cp's OEIS Frontend

A228463 Number of arrays of maxima of three adjacent elements of some length 8 0..n array.

%I A228463 #11 Sep 11 2018 09:45:44
%S A228463 27,183,736,2227,5615,12453,25096,46941,82699,138699,223224,346879,
%T A228463 522991,768041,1102128,1549465,2138907,2904511,3886128,5130027,
%U A228463 6689551,8625805,11008376,13916085,17437771,21673107,26733448,32742711,39838287
%N A228463 Number of arrays of maxima of three adjacent elements of some length 8 0..n array.
%H A228463 R. H. Hardin, <a href="/A228463/b228463.txt">Table of n, a(n) for n = 1..210</a>
%F A228463 Empirical: a(n) = (2/45)*n^6 + (8/15)*n^5 + (115/36)*n^4 + 8*n^3 + (1667/180)*n^2 + (149/30)*n + 1.
%F A228463 Conjectures from _Colin Barker_, Sep 11 2018: (Start)
%F A228463 G.f.: x*(27 - 6*x + 22*x^2 - 27*x^3 + 22*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A228463 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A228463 (End)
%e A228463 Some solutions for n=4:
%e A228463 ..4....4....4....3....1....4....4....4....4....1....4....4....0....1....2....0
%e A228463 ..2....4....4....1....0....2....2....2....2....0....4....2....1....1....1....0
%e A228463 ..0....4....4....0....2....0....1....3....1....0....2....0....1....1....1....0
%e A228463 ..0....3....1....1....3....0....3....3....0....2....2....1....2....0....0....1
%e A228463 ..0....3....0....4....3....0....4....3....3....2....2....1....3....0....1....1
%e A228463 ..2....3....4....4....3....1....4....3....4....3....2....1....4....4....2....4
%Y A228463 Row 6 of A228461.
%K A228463 nonn
%O A228463 1,1
%A A228463 _R. H. Hardin_, Aug 22 2013