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A166805 Number of n X 4 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. 0
3, 13, 33, 68, 124, 208, 328, 493, 713, 999, 1363, 1818, 2378, 3058, 3874, 4843, 5983, 7313, 8853, 10624, 12648, 14948, 17548, 20473, 23749, 27403, 31463, 35958, 40918, 46374, 52358, 58903, 66043, 73813, 82249, 91388, 101268, 111928, 123408, 135749, 148993 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..41.

FORMULA

a(n) = (n^4 + 10*n^3 + 35*n^2 + 50*n - 24)/24.

a(n) = (n^2 + 5*n - 2)*(n^2 + 5*n + 12)/24.

a(n) = (1/24)*(n+1)*(n+2)*(n+3)*(n+4) - 2. - Joerg Arndt, Apr 14 2011

G.f.: x*(3-2*x -2*x^2 +3*x^3 -x^4)/(1-x)^5. - Colin Barker, Jan 11 2012

E.g.f.: (1/24)*(-24 + 96*x + 72*x^2 + 16*x^3 + x^4)*exp(x) + 1. - G. C. Greubel, May 27 2016

EXAMPLE

Some solutions for n=4

...1.1.1.1...1.1.1.1...1.1.1.1...1.1.2.2...1.1.1.1...1.1.2.2...1.1.1.2

...1.1.1.1...1.1.2.2...1.1.1.1...1.2.2.2...1.1.1.1...1.1.2.2...1.1.1.2

...1.1.1.1...1.2.2.2...1.1.1.2...1.2.2.2...1.1.2.2...2.2.2.2...1.1.1.2

...2.2.2.2...1.2.2.2...1.1.2.2...2.2.2.2...2.2.2.2...2.2.2.2...1.2.2.2

------

...1.1.1.1...1.1.2.2...1.1.1.1...1.1.1.1...1.1.1.2...1.1.1.1...1.1.2.2

...1.1.1.2...1.1.2.2...1.2.2.2...1.1.1.1...2.2.2.2...1.1.1.2...2.2.2.2

...2.2.2.2...1.1.2.2...1.2.2.2...1.2.2.2...2.2.2.2...1.1.2.2...2.2.2.2

...2.2.2.2...1.1.2.2...2.2.2.2...2.2.2.2...2.2.2.2...1.2.2.2...2.2.2.2

MAPLE

a:= n-> binomial(n+4, 4)-2:

seq(a(n), n=1..50); # Alois P. Heinz, May 31 2012

MATHEMATICA

q=60; (Transpose[NestList[Accumulate, Range[q], q]]-2)[[5]] (* Vladimir Joseph Stephan Orlovsky, Apr 08 2011 *)

CROSSREFS

Cf. A063258.

Sequence in context: A032586 A147137 A146230 * A252979 A332366 A033943

Adjacent sequences: A166802 A166803 A166804 * A166806 A166807 A166808

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 21 2009

STATUS

approved

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Last modified December 7 07:00 EST 2022. Contains 358649 sequences. (Running on oeis4.)