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A190040 Number of nondecreasing arrangements of n+2 numbers in 0..8 with the last equal to 8 and each after the second equal to the sum of one or two of the preceding three. 1

%I

%S 13,24,40,65,105,164,246,349,472,617,786,981,1204,1457,1742,2061,2416,

%T 2809,3242,3717,4236,4801,5414,6077,6792,7561,8386,9269,10212,11217,

%U 12286,13421,14624,15897,17242,18661,20156,21729,23382,25117,26936,28841

%N Number of nondecreasing arrangements of n+2 numbers in 0..8 with the last equal to 8 and each after the second equal to the sum of one or two of the preceding three.

%C Column 8 of A190041.

%H R. H. Hardin, <a href="/A190040/b190040.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (1/3)*n^3 + 2*n^2 + (50/3)*n - 83 for n>6.

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

%F G.f.: x*(13 - 28*x + 22*x^2 - 3*x^3 + 2*x^4 - 2*x^5 - 6*x^7 + x^8 + 3*x^9) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.

%F (End)

%e Some solutions for n=3:

%e ..1....2....6....0....0....0....1....2....3....2....1....2....8....3....2....1

%e ..4....4....8....8....4....4....4....4....8....6....4....6....8....4....3....7

%e ..4....4....8....8....4....4....4....4....8....6....4....8....8....4....5....8

%e ..8....4....8....8....4....8....5....8....8....8....4....8....8....4....8....8

%e ..8....8....8....8....8....8....8....8....8....8....8....8....8....8....8....8

%Y Cf. A190041.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 04 2011

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Last modified October 28 16:41 EDT 2021. Contains 348329 sequences. (Running on oeis4.)