A052389 Number of 4-element intersecting families (with not necessarily distinct sets) of an n-element set.
0, 1, 9, 95, 1286, 20681, 360964, 6452825, 114920766, 2018035121, 34864971944, 593281456505, 9965368457746, 165615181710161, 2728984827320124, 44665923097267385, 727216852411490726, 11791672548220250801
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..825
- V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, 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 (83, -3052, 65670, -919413, 8804499, -58966886, 277278100, -904270136, 1982352768, -2749917312, 2142305280, -696729600).
Programs
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Magma
[(16^n - 6*12^n + 12*10^n - 9^n-10*8^n + 15*7^n - 24*6^n + 19*5^n + 5*4^n - 11*3^n + 6*2^n - 6)/24: n in [0..50]]; // G. C. Greubel, Oct 08 2017
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Mathematica
Table[(16^n - 6*12^n + 12*10^n - 9^n-10*8^n + 15*7^n - 24*6^n + 19*5^n + 5*4^n - 11*3^n + 6*2^n - 6)/24, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *) -
PARI
for(n=0,50, print1((16^n - 6*12^n + 12*10^n - 9^n-10*8^n + 15*7^n - 24*6^n + 19*5^n + 5*4^n - 11*3^n + 6*2^n - 6)/24, ", ")) \\ G. C. Greubel, Oct 08 2017
Formula
a(n) = (16^n - 6*12^n + 12*10^n - 9^n-10*8^n + 15*7^n - 24*6^n + 19*5^n + 5*4^n - 11*3^n + 6*2^n - 6)/24.
G.f.: x * (118224000*x^10 - 215558352*x^9 + 171543508*x^8 - 77761264*x^7 + 22230235*x^6 - 4199119*x^5 + 532266*x^4 - 44801*x^3 + 2400*x^2 - 74*x + 1) / ( (x-1) * (2*x-1) * (3*x-1) * (4*x-1) * (5*x-1) * (6*x-1) * (7*x-1) * (8*x-1) * (9*x-1) * (10*x-1) * (12*x-1) * (16*x-1) ). - Colin Barker, Jul 30 2012