A212865 - OEIS

%I #9 Sep 09 2019 02:28:49

%S 0,5,9,15,22,32,40,59,74,97,124,159,188,229,260,301,347,415,477,559,

%T 630,715,801,897,987,1106,1214,1342,1471,1623,1760,1934,2099,2287,

%U 2475,2683,2878,3116,3334,3581,3832,4115,4377,4681,4968,5283,5605,5965,6310,6707

%N Number of nondecreasing sequences of n 1..5 integers with no element dividing the sequence sum.

%C Column 5 of A212868.

%H R. H. Hardin, <a href="/A212865/b212865.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-5) +2*a(n-6) -2*a(n-7) -2*a(n-8) +2*a(n-9) +a(n-10) -a(n-12) -2*a(n-13) +2*a(n-14) +2*a(n-15) -2*a(n-16) -a(n-17) +2*a(n-19) +a(n-20) -4*a(n-21) +a(n-22) +2*a(n-23) -a(n-25) -2*a(n-26) +2*a(n-27) +2*a(n-28) -2*a(n-29) -a(n-30) +a(n-32) +2*a(n-33) -2*a(n-34) -2*a(n-35) +2*a(n-36) +a(n-37) -2*a(n-39) +2*a(n-41) -a(n-42).

%F If the above empirical recurrence by _R. H. Hardin_ is correct, then the denominator of the g.f. (that determines the above recurrence) equals (1-x)^2*(1-x^2)*(1-x^12)*(1-x^15)*(1-x^20)/((1-x^4)*(1-x^5)). - _Petros Hadjicostas_, Sep 09 2019

%e Some solutions for n=8:

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

%e ..2....3....2....3....3....4....5....3....3....2....4....2....3....5....3....2

%e ..2....3....2....3....3....4....5....4....4....3....4....3....3....5....3....2

%e ..2....3....3....3....3....4....5....4....4....3....4....3....3....5....3....4

%e ..2....3....5....3....3....4....5....4....5....4....4....3....3....5....4....4

%e ..3....4....5....3....3....4....5....4....5....5....4....4....3....5....4....5

%e ..3....5....5....3....3....4....5....5....5....5....4....4....4....5....5....5

%e ..3....5....5....3....4....5....5....5....5....5....5....4....4....5....5....5

%K nonn

%O 1,2

%A _R. H. Hardin_, May 29 2012