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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A254831 A145013 A096943 * A210367 A261347 A079909

Adjacent sequences:  A166807 A166808 A166809 * A166811 A166812 A166813

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 21 2009

STATUS

approved

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Last modified May 23 18:24 EDT 2017. Contains 286926 sequences.