A211562 - OEIS

%I #10 Jul 19 2018 05:50:26

%S 5,14,36,81,162,295,499,796,1211,1772,2510,3459,4656,6141,7957,10150,

%T 12769,15866,19496,23717,28590,34179,40551,47776,55927,65080,75314,

%U 86711,99356,113337,128745,145674,164221,184486,206572,230585,256634,284831

%N Number of nonnegative integer arrays of length n+2 with new values 0 upwards introduced in order, and containing the value n-1.

%C Row 3 of A211561.

%H R. H. Hardin, <a href="/A211562/b211562.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/8)*n^4 + (5/12)*n^3 + (7/8)*n^2 + (19/12)*n + 2.

%F Empirical: a(n) = sum{j in n..n+2}stirling2(n+2,j).

%F Conjectures from _Colin Barker_, Jul 19 2018: (Start)

%F G.f.: x*(5 - 11*x + 16*x^2 - 9*x^3 + 2*x^4) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=5:

%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1

%e ..2....2....2....2....2....2....0....0....2....2....2....1....2....2....2....2

%e ..3....1....2....3....3....0....2....2....2....0....3....2....3....3....3....3

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

%e ..4....3....3....1....0....2....3....3....4....3....3....2....5....3....2....0

%e ..4....4....4....4....4....4....4....4....1....4....1....4....4....5....4....1

%Y Cf. A211561.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 15 2012