A052391 Number of 4-element intersecting families (of distinct sets) whose union is an n-element set.

0, 0, 4, 349, 9985, 213230, 4000444, 69940479, 1170549895, 19024433560, 302846958634, 4748624978009, 73628721516805, 1132119741733890, 17298702716660824, 263082403948681939, 3986935934969727715

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..845

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 (71, -2205, 39495, -452523, 3473673, -18166175, 64427005, -150923976, 220549356, -178819920, 59875200).

Formula

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

G.f.: x^3*(14968800*x^8 - 25752870*x^7 + 16968966*x^6 - 5759365*x^5 + 1095624*x^4 - 115860*x^3 + 5974*x^2 - 65*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)*(11*x-1)*(15*x-1)). - Colin Barker, Jul 30 2012

Mathematica

Table[(15^n - 6*11^n + 12*9^n - 8^n - 22*7^n + 15*6^n + 12*5^n - 17*4^n + 17*3^n - 11*2^n - 6)/4!, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
LinearRecurrence[{71, -2205, 39495, -452523, 3473673, -18166175, 64427005, -150923976, 220549356, -178819920, 59875200}, {0, 0, 4, 349, 9985, 213230, 4000444, 69940479, 1170549895, 19024433560, 302846958634}, 20] (* Harvey P. Dale, May 20 2018 *)

Prog

(PARI) for(n=0, 50, print1((15^n - 6*11^n + 12*9^n - 8^n - 22*7^n + 15*6^n + 12*5^n - 17*4^n + 17*3^n - 11*2^n - 6)/24, ", ")) \\ G. C. Greubel, Oct 08 2017
(Magma) [(15^n - 6*11^n + 12*9^n - 8^n - 22*7^n + 15*6^n + 12*5^n - 17*4^n + 17*3^n - 11*2^n - 6)/24: n in [0..50]]; // G. C. Greubel, Oct 08 2017

Crossrefs

Cf. A051181, A053152, A053153.

Sequence in context: A283101 A074844 A225207 * A214182 A214233 A334359

Adjacent sequences: A052388 A052389 A052390 * A052392 A052393 A052394

Keyword

nonn,easy

Author

Vladeta Jovovic, Goran Kilibarda, Mar 11 2000

Status

approved