cp's OEIS Frontend

A242145 Number of length 1+5 0..n arrays with no consecutive six elements summing to more than 3*n.

%I A242145 #10 Oct 31 2018 21:50:15
%S A242145 42,435,2338,8688,25494,63490,140148,282051,527626,930237,1561638,
%T A242145 2515786,3913014,5904564,8677480,12459861,17526474,24204727,32881002,
%U A242145 44007348,58108534,75789462,97742940,124757815,157727466,197658657
%N A242145 Number of length 1+5 0..n arrays with no consecutive six elements summing to more than 3*n.
%H A242145 R. H. Hardin, <a href="/A242145/b242145.txt">Table of n, a(n) for n = 1..210</a>
%F A242145 Empirical: a(n) = (1/2)*n^6 + (131/40)*n^5 + (71/8)*n^4 + (103/8)*n^3 + (85/8)*n^2 + (97/20)*n + 1.
%F A242145 Conjectures from _Colin Barker_, Oct 31 2018: (Start)
%F A242145 G.f.: x*(42 + 141*x + 175*x^2 - 13*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A242145 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 A242145 (End)
%e A242145 Some solutions for n=4:
%e A242145   2  4  2  3  0  2  1  1  0  2  4  0  0  0  1  3
%e A242145   2  0  1  0  0  4  2  2  0  1  1  3  0  1  2  0
%e A242145   1  2  1  1  4  2  1  3  1  1  1  0  0  0  3  0
%e A242145   3  3  4  2  4  1  3  0  1  4  0  0  0  1  3  2
%e A242145   1  2  3  3  1  1  2  4  0  2  1  2  0  2  1  1
%e A242145   1  0  0  1  3  2  2  2  4  1  1  3  0  4  2  2
%Y A242145 Row 1 of A242144.
%K A242145 nonn
%O A242145 1,1
%A A242145 _R. H. Hardin_, May 05 2014