A166761 Number of n X 3 1..2 arrays containing at least one of each value, and all equal values connected.

4, 30, 106, 292, 712, 1618, 3518, 7432, 15404, 31526, 63986, 129164, 259824, 521498, 1045254, 2093232, 4189716, 8383278, 16771066, 33547380, 67100824, 134208610, 268425166, 536859352, 1073728892, 2147469238, 4294951298, 8589916892

Offset: 1

Author

R. H. Hardin, Oct 21 2009

Keywords

• nonn

Examples

			Some solutions for n=4
...2.2.2...2.2.2...1.1.2...1.1.1...2.1.1...1.1.1...1.2.2...1.2.2...1.1.1
...2.1.1...1.2.2...1.2.2...2.2.1...2.2.2...2.1.1...1.2.2...1.2.2...1.2.1
...2.1.1...1.2.1...1.2.2...2.2.1...2.2.2...2.2.1...1.1.2...1.1.2...1.2.1
...2.2.1...1.1.1...1.1.2...2.2.1...2.2.2...2.2.2...2.2.2...1.1.1...1.1.1
------
...1.2.2...2.2.2...1.1.2...1.1.1...1.1.1...1.1.2...1.2.2...1.2.2...1.1.1
...1.1.2...2.1.2...1.1.2...2.2.1...1.1.2...1.1.2...1.1.2...1.2.1...1.1.1
...1.1.2...1.1.1...1.2.2...2.2.1...1.1.2...1.1.2...1.1.2...1.1.1...2.2.1
...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...2.2.2...1.1.1...2.1.1
		

Links

• R. H. Hardin, Table of n, a(n) for n=1..41
• Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-9,2)

Crossrefs

Twice row 3 of A378932.

Cf. A378933.

Formula

Empirical: a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) -9*a(n-4) + 2*a(n-5).

From G. C. Greubel, May 26 2016: (Start)

Empirical a(n) = (3*2^(n + 5) - 2*n^3 - 9*n^2 - 73*n - 96)/3.

Empirical G.f.: (1/3)*( 96/(1 - 2*x) + 6*(-16 + 34*x - 25*x^2 + 5*x^3)/(1 - x)^4 ).

Empirical E.g.f.: (1/3)*(96*exp(x) - (96 + 84*x + 15*x^2 + 2*x^3 ) )*exp(x). (End)

From Andrew Howroyd, Dec 12 2024: (Start)

The above empirical formulas are correct.

a(n) = 2*A378933(n).

(End)