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.

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

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