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

1,1

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

Links

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

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

Example

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

Maple

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

Prog

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

Crossrefs

Sequence in context: A360350 A145013 A096943 * A210367 A261347 A079909

Adjacent sequences: A166807 A166808 A166809 * A166811 A166812 A166813

Keyword

nonn

Author

R. H. Hardin, Oct 21 2009

Status

approved