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
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).
Crossrefs
Cf. A051180.
Programs
-
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
-
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 *) -
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
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