A051181 Number of 4-element intersecting families of an n-element set.

0, 0, 0, 4, 365, 11770, 278455, 5715094, 108498285, 1963243930, 34404675635, 589459538734, 9933916068505, 165358097339890, 2726894329246815, 44648990949187174, 727080119853611525, 11790570902483264650, 190587735542474633995, 3073193346666282232414

Offset

0,4

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).

Formula

a(n) = (1/4!)*(16^n - 6*12^n + 12*10^n - 9^n - 22*8^n + 15*7^n + 12*6^n - 17*5^n + 17*4^n - 11*3^n - 6*2^n + 6).

G.f.: -x^3*(64667520*x^8 - 81966960*x^7 + 42070268*x^6 - 11421992*x^5 + 1766529*x^4 - 152845*x^3 + 6317*x^2 - 33*x - 4)/((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

Mathematica

Table[1/4! (16^n - 6*12^n + 12*10^n - 9^n - 22*8^n + 15*7^n + 12*6^n - 17*5^n + 17*4^n - 11*3^n - 6*2^n + 6), {n, 0, 50}] (* G. C. Greubel, Oct 06 2017 *)
LinearRecurrence[{83, -3052, 65670, -919413, 8804499, -58966886, 277278100, -904270136, 1982352768, -2749917312, 2142305280, -696729600}, {0, 0, 0, 4, 365, 11770, 278455, 5715094, 108498285, 1963243930, 34404675635, 589459538734}, 20] (* Harvey P. Dale, Jul 04 2019 *)

Prog

(PARI) for(n=0, 25, print1((1/4!)*(16^n-6*12^n+12*10^n-9^n-22*8^n+15*7^n +12*6^n-17*5^n+17*4^n-11*3^n-6*2^n+6), ", ")) \\ G. C. Greubel, Oct 06 2017

Crossrefs

Cf. A036239, A051180-A051185.

Sequence in context: A051955 A177114 A109760 * A326996 A154682 A292195

Adjacent sequences: A051178 A051179 A051180 * A051182 A051183 A051184

Keyword

nonn,easy

Author

Vladeta Jovovic, Goran Kilibarda

Extensions

More terms from Harvey P. Dale, Jul 04 2019

Status

approved