|
%I #12 Jun 02 2018 10:34:58
%S 2,42,228,776,2046,4578,9128,16704,28602,46442,72204,108264,157430,
%T 222978,308688,418880,558450,732906,948404,1211784,1530606,1913186,
%U 2368632,2906880,3538730,4275882,5130972,6117608,7250406,8545026
%N Number of 3 X 3 0..n arrays with row and column sums one greater than the previous row and column.
%C Row 3 of A202864.
%H R. H. Hardin, <a href="/A202865/b202865.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (3/10)*n^5 + (3/2)*n^4 + (3/2)*n^3 - (1/2)*n^2 - (4/5)*n.
%F Conjectures from _Colin Barker_, Jun 02 2018: (Start)
%F G.f.: 2*x*(1 + 15*x + 3*x^2 - x^3) / (1 - x)^6.
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F (End)
%e Some solutions for n=7:
%e 6 5 2 2 5 4 1 7 4 4 4 2 2 2 1 6 3 0 2 6 2
%e 6 2 6 3 5 4 5 1 7 1 4 6 0 0 6 2 2 6 3 4 4
%e 1 7 7 6 2 5 6 5 3 5 3 4 3 4 0 1 5 5 5 1 6
%Y Cf. A202864.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 25 2011
|
