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 A190036 Number of nondecreasing arrangements of n+2 numbers in 0..4 with the last equal to 4 and each after the second equal to the sum of one or two of the preceding three. 1

%I

%S 7,12,18,27,39,53,69,87,107,129,153,179,207,237,269,303,339,377,417,

%T 459,503,549,597,647,699,753,809,867,927,989,1053,1119,1187,1257,1329,

%U 1403,1479,1557,1637,1719,1803,1889,1977,2067,2159,2253,2349,2447,2547,2649

%N Number of nondecreasing arrangements of n+2 numbers in 0..4 with the last equal to 4 and each after the second equal to the sum of one or two of the preceding three.

%C Column 4 of A190041.

%H R. H. Hardin, <a href="/A190036/b190036.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = n^2 + 3*n - 1 for n>3.

%F Conjectures from _Colin Barker_, May 04 2018: (Start)

%F G.f.: x*(7 - 9*x + 3*x^2 + 2*x^3 - x^5) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

%F (End)

%e Some solutions for n=3:

%e 2 1 1 3 1 2 0 1 0 1 1 2 0 1 1 4

%e 2 1 1 4 4 2 2 2 2 3 2 2 4 2 3 4

%e 4 2 2 4 4 2 2 2 2 3 2 2 4 3 4 4

%e 4 2 3 4 4 4 2 2 4 4 4 2 4 4 4 4

%e 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

%Y Cf. A190041.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 04 2011

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)