cp's OEIS Frontend

A228212 Number of second differences of arrays of length n + 2 of numbers in 0..2.

%I A228212 #10 Sep 29 2023 07:59:58
%S A228212 9,49,199,665,2059,6305,19171,58025,175099,527345,1586131,4766585,
%T A228212 14316139,42981185,129009091,387158345,1161737179,3485735825,
%U A228212 10458256051,31376865305,94134790219,282412759265,847255055011,2541798719465
%N A228212 Number of second differences of arrays of length n + 2 of numbers in 0..2.
%H A228212 R. H. Hardin, <a href="/A228212/b228212.txt">Table of n, a(n) for n = 1..210</a>
%F A228212 Empirical: a(n) = 5*a(n-1) -6*a(n-2) = A001047(n+2) for n>5.
%F A228212 Conjectures from _Colin Barker_, Sep 09 2018: (Start)
%F A228212 G.f.: x*(9 + 4*x + 8*x^2 - 36*x^3 - 72*x^4) / ((1 - 2*x)*(1 - 3*x)).
%F A228212 a(n) = 3^(2+n) - 2^(2+n) for n>3.
%F A228212 (End)
%e A228212 Some solutions for n=4:
%e A228212 ..3....3...-4....0....1....0...-3...-1...-2....4....0...-4....0....0....3....2
%e A228212 .-1...-2....3....3...-1...-2....2....0....4...-4....0....3...-2...-1....0...-1
%e A228212 .-1...-1....0...-3....0....1...-2....1...-2....4....1....0....0....0...-3....0
%e A228212 ..2....1...-2....2....0....1....0...-3...-2...-2...-3...-3....3...-1....3....1
%Y A228212 Column 2 of A228218.
%K A228212 nonn
%O A228212 1,1
%A A228212 _R. H. Hardin_, Aug 16 2013