A053155 Number of 3-element intersecting families (with not necessarily distinct sets) of an n-element set.

0, 1, 7, 50, 397, 3366, 29197, 253030, 2170357, 18385046, 153927037, 1275981510, 10492253317, 85727548726, 696964520077, 5644579061990, 45579645264277, 367223771048406, 2953549834748317, 23724145930814470, 190373553357763237

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..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 (29,-343,2135,-7504,14756,-14832,5760).

Formula

a(n) = (8^n - 3*6^n + 3*5^n + 2*4^n - 3*3^n + 2*2^n - 2)/6.

G.f.: x*(1224*x^5-1562*x^4+787*x^3-190*x^2+22*x-1)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - Colin Barker, Jul 29 2012

a(n) = 29*a(n-1) - 343*a(n-2) + 2135*a(n-3) - 7504*a(n-4) + 14756*a(n-5) - 14832*a(n-6) + 5760*a(n-7) for n > 6. - Wesley Ivan Hurt, Oct 06 2017

Maple

A053155:=n->(8^n - 3*6^n + 3*5^n + 2*4^n - 3*3^n + 2*2^n - 2)/6: seq(A053155(n), n=0..30); # Wesley Ivan Hurt, Oct 06 2017

Mathematica

Table[(8^n - 3*6^n + 3*5^n + 2*4^n - 3*3^n + 2*2^n - 2)/6, {n, 0, 50}] (* G. C. Greubel, Oct 06 2017 *)
LinearRecurrence[{29, -343, 2135, -7504, 14756, -14832, 5760}, {0, 1, 7, 50, 397, 3366, 29197}, 30] (* Vincenzo Librandi, Oct 07 2017 *)

Prog

(PARI) for(n=0, 50, print1((8^n - 3*6^n + 3*5^n + 2*4^n - 3*3^n + 2*2^n - 2)/6, ", ")) \\ G. C. Greubel, Oct 06 2017
(Magma) [(8^n - 3*6^n + 3*5^n + 2*4^n - 3*3^n + 2*2^n - 2)/6: n in [0..50]]; // G. C. Greubel, Oct 06 2017

Crossrefs

Cf. A051180.

Sequence in context: A065429 A346846 A005460 * A367235 A355171 A266432

Adjacent sequences: A053152 A053153 A053154 * A053156 A053157 A053158

Keyword

easy,nonn

Author

Vladeta Jovovic, Goran Kilibarda, Feb 28 2000

Status

approved