A212864 - OEIS

%I #8 Jul 21 2018 15:52:13

%S 0,2,3,5,6,9,12,15,17,22,26,30,34,40,45,51,56,63,70,77,83,92,100,108,

%T 116,126,135,145,154,165,176,187,197,210,222,234,246,260,273,287,300,

%U 315,330,345,359,376,392,408,424,442,459,477,494,513,532,551,569,590,610,630,650

%N Number of nondecreasing sequences of n 1..4 integers with no element dividing the sequence sum.

%C Column 4 of A212868.

%H R. H. Hardin, <a href="/A212864/b212864.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + a(n-3) - a(n-5) - a(n-7) + a(n-8).

%F Empirical g.f.: x^2*(2 + x + 2*x^2 - x^3) / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2)). - _Colin Barker_, Jul 21 2018

%e All solutions for n=8:

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

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

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

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

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

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

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

%e ..4....3....4....4....3....3....4....4....4....4....4....4....4....4....4

%Y Cf. A212868.

%K nonn

%O 1,2

%A _R. H. Hardin_, May 29 2012