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A053152 Number of 2-element intersecting families whose union is an n-element set. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

V. Jovovic, 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, 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 xrange(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.

Sequence in context: A198016 A082114 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

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Last modified November 14 20:15 EST 2019. Contains 329130 sequences. (Running on oeis4.)