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A190035 Number of nondecreasing arrangements of n+2 numbers in 0..3 with the last equal to 3 and each after the second equal to the sum of one or two of the preceding three.

%I A190035 #11 Aug 25 2025 10:12:06
%S A190035 5,7,10,14,18,22,26,30,34,38,42,46,50,54,58,62,66,70,74,78,82,86,90,
%T A190035 94,98,102,106,110,114,118,122,126,130,134,138,142,146,150,154,158,
%U A190035 162,166,170,174,178,182,186,190,194,198,202,206,210,214,218,222,226,230,234,238
%N A190035 Number of nondecreasing arrangements of n+2 numbers in 0..3 with the last equal to 3 and each after the second equal to the sum of one or two of the preceding three.
%C A190035 Column 3 of A190041.
%H A190035 R. H. Hardin, <a href="/A190035/b190035.txt">Table of n, a(n) for n = 1..200</a>
%F A190035 Empirical: a(n) = 4*n - 2 for n>2.
%F A190035 Conjectures from _Colin Barker_, May 03 2018: (Start)
%F A190035 G.f.: x*(5 - 3*x + x^2 + x^3) / (1 - x)^2.
%F A190035 a(n) = 2*a(n-1) - a(n-2) for n>4.
%F A190035 (End)
%e A190035 All solutions for n=4:
%e A190035 ..1....1....0....3....2....0....1....0....1....1....0....1....1....1
%e A190035 ..1....1....3....3....3....1....1....1....2....1....1....2....3....1
%e A190035 ..2....1....3....3....3....1....2....1....3....1....1....2....3....1
%e A190035 ..2....1....3....3....3....2....3....2....3....2....1....3....3....2
%e A190035 ..3....2....3....3....3....2....3....3....3....3....2....3....3....2
%e A190035 ..3....3....3....3....3....3....3....3....3....3....3....3....3....3
%Y A190035 Cf. A190041, A073760, A016825.
%K A190035 nonn,changed
%O A190035 1,1
%A A190035 _R. H. Hardin_, May 04 2011