A052390 Number of 4-element intersecting families (with not necessarily distinct sets) whose union is an n-element set.
1, 7, 71, 956, 15116, 254397, 4318511, 72331966, 1188180386, 19152566087, 303768582701, 4755204310776, 73675434833456, 1132450098258577, 17301032324486891, 263098797953058386, 3987051131522775326
Offset: 1
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).
Programs
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Magma
[(15^n - 6*11^n + 12*9^n - 8^n - 10*7^n + 15*6^n - 24*5^n + 19*4^n + 5*3^n - 11*2^n + 6)/24: n in [1..50]]; // G. C. Greubel, Oct 08 2017
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Mathematica
Table[(15^n - 6*11^n + 12*9^n - 8^n - 10*7^n + 15*6^n - 24*5^n + 19*4^n + 5*3^n - 11*2^n + 6)/4!, {n, 1, 50}] (* G. C. Greubel, Oct 08 2017 *) -
PARI
for(n=1,50, print1((15^n - 6*11^n + 12*9^n - 8^n - 10*7^n + 15*6^n - 24*5^n + 19*4^n + 5*3^n - 11*2^n + 6)/4!, ", ")) \\ G. C. Greubel, Oct 08 2017
Formula
a(n) = (15^n - 6*11^n + 12*9^n - 8^n - 10*7^n + 15*6^n - 24*5^n + 19*4^n + 5*3^n - 11*2^n + 6)/4!.
G.f.: -x * (14968800*x^10 - 34931250*x^9 + 36757686*x^8 - 21625925*x^7 + 7809481*x^6 - 1821016*x^5 + 279853*x^4 - 28145*x^3 + 1779*x^2 - 64*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)*(11*x-1)*(15*x-1)). - Colin Barker, Jul 30 2012