A053152 Number of 2-element intersecting families whose union is an n-element set.

0, 2, 9, 32, 105, 332, 1029, 3152, 9585, 29012, 87549, 263672, 793065, 2383292, 7158069, 21490592, 64504545, 193579172, 580868589, 1742867912, 5229128025, 15688432652, 47067395109, 141206379632, 423627527505, 1270899359732, 3812731633629, 11438262009752

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, (in Russian), Diskretnaya Matematika, 11 (1999), no. 4, 127-138.

V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Formula

a(n) = (1/2!)*(3^n-2^n-1).

From Colin Barker, Jun 26 2012: (Start)

a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3).

G.f.: x^2*(2-3*x)/((1-x)*(1-2*x)*(1-3*x)). (End)

a(n) = floor((3^n-2^n)/2). - Wesley Ivan Hurt, Mar 16 2015

Maple

A053152:=n->floor((3^n-2^n)/2): seq(A053152(n), n=1..30); # Wesley Ivan Hurt, Mar 19 2015

Mathematica

CoefficientList[Series[x (2 - 3 x) / ((1 - x) (1 - 2 x) (1 - 3 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 17 2015 *)
LinearRecurrence[{6, -11, 6}, {0, 2, 9}, 50] (* G. C. Greubel, Oct 06 2017 *)

Prog

(Sage) [(3^n - 1)/2-2^(n-1) for n in range(1, 27)] # Zerinvary Lajos, Jun 05 2009
(Magma) [Floor((3^n-2^n)/2): n in [1..30]]; // Vincenzo Librandi, Mar 17 2015
(PARI) for(n=1, 50, print1((1/2)*(3^n -2^n -1), ", ")) \\ G. C. Greubel, Oct 06 2017

Crossrefs

Cf. A036239, A064686 (first differences).

Sequence in context: A082114 A332870 A074084 * A077644 A292482 A053369

Adjacent sequences: A053149 A053150 A053151 * A053153 A053154 A053155

Keyword

easy,nonn

Author

Vladeta Jovovic, Goran Kilibarda, Feb 28 2000

Extensions

More terms from James A. Sellers, Mar 01 2000

a(27)-a(28) from Vincenzo Librandi, Mar 17 2015

Status

approved