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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. 1

%I

%S 5,7,10,14,18,22,26,30,34,38,42,46,50,54,58,62,66,70,74,78,82,86,90,

%T 94,98,102,106,110,114,118,122,126,130,134,138,142,146,150,154,158,

%U 162,166,170,174,178,182,186,190,194,198,202,206,210,214,218,222,226,230,234,238

%N 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 Column 3 of A190041.

%H R. H. Hardin, <a href="/A190035/b190035.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 4*n - 2 for n>2.

%F Conjectures from _Colin Barker_, May 03 2018: (Start)

%F G.f.: x*(5 - 3*x + x^2 + x^3) / (1 - x)^2.

%F a(n) = 2*a(n-1) - a(n-2) for n>4.

%F (End)

%e All solutions for n=4:

%e ..1....1....0....3....2....0....1....0....1....1....0....1....1....1

%e ..1....1....3....3....3....1....1....1....2....1....1....2....3....1

%e ..2....1....3....3....3....1....2....1....3....1....1....2....3....1

%e ..2....1....3....3....3....2....3....2....3....2....1....3....3....2

%e ..3....2....3....3....3....2....3....3....3....3....2....3....3....2

%e ..3....3....3....3....3....3....3....3....3....3....3....3....3....3

%Y Cf. A190041.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 04 2011

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Last modified December 3 15:47 EST 2021. Contains 349464 sequences. (Running on oeis4.)