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Number of 4-element intersecting families (with not necessarily distinct sets) of an n-element set.
1

%I #24 Jan 29 2023 18:59:42

%S 0,1,9,95,1286,20681,360964,6452825,114920766,2018035121,34864971944,

%T 593281456505,9965368457746,165615181710161,2728984827320124,

%U 44665923097267385,727216852411490726,11791672548220250801

%N Number of 4-element intersecting families (with not necessarily distinct sets) of an n-element set.

%H G. C. Greubel, <a href="/A052389/b052389.txt">Table of n, a(n) for n = 0..825</a>

%H V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.4213/dm398">On the number of Boolean functions in the Post classes F^{mu}_8</a>, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.

%H V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.1515/dma.1999.9.6.593">On the number of Boolean functions in the Post classes F^{mu}_8</a>, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (83, -3052, 65670, -919413, 8804499, -58966886, 277278100, -904270136, 1982352768, -2749917312, 2142305280, -696729600).

%F 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.

%F 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

%t 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 *)

%o (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

%o (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

%Y Cf. A051181, A053154, A053155.

%K nonn,easy

%O 0,3

%A _Vladeta Jovovic_, Goran Kilibarda, Mar 11 2000