A055485 Number of unlabeled 3-element intersecting families (with distinct sets) of an n-element set.

4, 19, 61, 157, 353, 717, 1355, 2412, 4094, 6676, 10524, 16108, 24036, 35063, 50135, 70409, 97295, 132485, 178011, 236268, 310086, 402768, 518158, 660692, 835486, 1048379, 1306039, 1616025, 1986887, 2428245, 2950913, 3566968, 4289896

Offset: 3

Author

Vladeta Jovovic, Goran Kilibarda, Jul 03 2000

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..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 (3,1,-9,0,12,7,-15,-16,16,15,-7,-12,0,9,-1,-3,1).

Crossrefs

Cf. A051180 (labeled case), A005783.

Programs

Mathematica

Rest[Rest[Rest[CoefficientList[Series[-x^3*(x^8 + x^7 - 3*x^6 - x^5 + x^4 + 3*x^3 - x^2 - 3*x - 4)/((x^3 - 1)^2*(x^2 - 1)^2*(x - 1)^4), {x,0,50}], x]]]] (* G. C. Greubel, Oct 06 2017 *)
LinearRecurrence[{3, 1, -9, 0, 12, 7, -15, -16, 16, 15, -7, -12, 0, 9, -1, -3, 1}, {4, 19, 61, 157, 353, 717, 1355, 2412, 4094, 6676, 10524, 16108, 24036, 35063, 50135, 70409, 97295}, 33] (* Vincenzo Librandi, Oct 07 2017 *)

PARI

x='x+O('x^50); Vec(-x^3*(x^8+x^7-3*x^6-x^5+x^4+3*x^3-x^2-3*x-4)/((x^3-1)^2*(x^2-1)^2*(x-1)^4)) \\ G. C. Greubel, Oct 06 2017

Formula

G.f.: -x^3*(x^8+x^7-3*x^6-x^5+x^4+3*x^3-x^2-3*x-4)/((x^3-1)^2*(x^2-1)^2*(x-1)^4).

Extensions

More terms from James Sellers, Jul 04 2000