A166810 Number of n X 6 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.

5, 26, 82, 208, 460, 922, 1714, 3001, 5003, 8006, 12374, 18562, 27130, 38758, 54262, 74611, 100945, 134594, 177098, 230228, 296008, 376738, 475018, 593773, 736279, 906190, 1107566, 1344902, 1623158, 1947790, 2324782, 2760679, 3262621, 3838378, 4496386, 5245784, 6096452, 7059050, 8145058, 9366817

Offset: 1

Author

R. H. Hardin, Oct 21 2009

Keywords

• nonn

Comments

This sequence (and A166812, A166813) correspond to k-tuples x with 0<= x(i+1) <= x(i) <= k except (0,0,0..) and (k,k,k...), where x(i) is the index of the first 2 in row i of the array (or 0 if none); the number of those are the binomials minus 2. - Robert Israel, Nov 23 2015

Examples

			Some solutions for n=4
...1.1.1.1.1.2...1.1.1.1.2.2...1.1.1.1.1.1...1.1.1.1.1.1...1.1.1.1.1.1
...1.1.1.1.1.2...1.1.1.1.2.2...1.1.1.1.1.1...1.1.1.1.1.2...1.1.1.1.1.2
...1.1.1.1.2.2...1.1.1.1.2.2...1.1.1.1.1.2...1.1.1.2.2.2...1.1.1.1.1.2
...1.1.1.2.2.2...1.1.1.1.2.2...1.1.1.1.2.2...2.2.2.2.2.2...1.1.1.1.1.2
------
...1.1.1.1.1.2...1.1.1.2.2.2...1.1.1.1.1.2...1.1.1.1.2.2...1.1.1.1.1.2
...1.1.2.2.2.2...1.1.2.2.2.2...1.1.1.1.2.2...1.1.1.1.2.2...1.1.1.1.1.2
...1.2.2.2.2.2...1.1.2.2.2.2...1.1.1.1.2.2...1.2.2.2.2.2...1.1.2.2.2.2
...1.2.2.2.2.2...1.1.2.2.2.2...1.1.2.2.2.2...1.2.2.2.2.2...1.1.2.2.2.2
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

seq(binomial(n+6,6)-2, n=1..100); # Robert Israel, Nov 24 2015

PARI

Vec(1-2/(1-x)+1/(1-x)^7 + O(x^100)) \\ Altug Alkan, Nov 24 2015

Formula

a(n) = A000579(n+6)-2. - R. J. Mathar, Nov 24 2015

G.f.: 1 - 2/(1-x) + 1/(1-x)^7. - Robert Israel, Nov 24 2015