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A211562 Number of nonnegative integer arrays of length n+2 with new values 0 upwards introduced in order, and containing the value n-1.

%I A211562 #10 Jul 19 2018 05:50:26
%S A211562 5,14,36,81,162,295,499,796,1211,1772,2510,3459,4656,6141,7957,10150,
%T A211562 12769,15866,19496,23717,28590,34179,40551,47776,55927,65080,75314,
%U A211562 86711,99356,113337,128745,145674,164221,184486,206572,230585,256634,284831
%N A211562 Number of nonnegative integer arrays of length n+2 with new values 0 upwards introduced in order, and containing the value n-1.
%C A211562 Row 3 of A211561.
%H A211562 R. H. Hardin, <a href="/A211562/b211562.txt">Table of n, a(n) for n = 1..210</a>
%F A211562 Empirical: a(n) = (1/8)*n^4 + (5/12)*n^3 + (7/8)*n^2 + (19/12)*n + 2.
%F A211562 Empirical: a(n) = sum{j in n..n+2}stirling2(n+2,j).
%F A211562 Conjectures from _Colin Barker_, Jul 19 2018: (Start)
%F A211562 G.f.: x*(5 - 11*x + 16*x^2 - 9*x^3 + 2*x^4) / (1 - x)^5.
%F A211562 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 A211562 (End)
%e A211562 Some solutions for n=5:
%e A211562 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A211562 ..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
%e A211562 ..2....2....2....2....2....2....0....0....2....2....2....1....2....2....2....2
%e A211562 ..3....1....2....3....3....0....2....2....2....0....3....2....3....3....3....3
%e A211562 ..0....1....1....3....2....3....2....0....3....1....4....3....4....4....1....4
%e A211562 ..4....3....3....1....0....2....3....3....4....3....3....2....5....3....2....0
%e A211562 ..4....4....4....4....4....4....4....4....1....4....1....4....4....5....4....1
%Y A211562 Cf. A211561.
%K A211562 nonn
%O A211562 1,1
%A A211562 _R. H. Hardin_, Apr 15 2012