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A190039 Number of nondecreasing arrangements of n+2 numbers in 0..7 with the last equal to 7 and each after the second equal to the sum of one or two of the preceding three. 1

%I

%S 11,17,22,31,43,60,80,100,120,140,160,180,200,220,240,260,280,300,320,

%T 340,360,380,400,420,440,460,480,500,520,540,560,580,600,620,640,660,

%U 680,700,720,740,760,780,800,820,840,860,880,900,920,940,960,980,1000,1020

%N Number of nondecreasing arrangements of n+2 numbers in 0..7 with the last equal to 7 and each after the second equal to the sum of one or two of the preceding three.

%C Column 7 of A190041.

%H R. H. Hardin, <a href="/A190039/b190039.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 20*n - 60 for n>5.

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

%F G.f.: x*(11 - 5*x - x^2 + 4*x^3 + 3*x^4 + 5*x^5 + 3*x^6) / (1 - x)^2.

%F a(n) = 2*a(n-1) - a(n-2) for n>7.

%F (End)

%e Some solutions for n=3:

%e 3 1 1 6 7 2 1 1 2 0 2 1 1 2 5 3

%e 4 6 3 7 7 3 3 3 5 7 5 6 2 7 7 4

%e 7 7 4 7 7 5 4 4 7 7 5 6 3 7 7 4

%e 7 7 5 7 7 7 4 7 7 7 7 7 4 7 7 7

%e 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

%Y Cf. A190041.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 04 2011

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Last modified October 20 16:07 EDT 2021. Contains 348111 sequences. (Running on oeis4.)