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Revision History for A052391 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Number of 4-element intersecting families (of distinct sets) whose union is an n-element set.
(history; published version)
#21 by Charles R Greathouse IV at Thu Sep 08 08:44:59 EDT 2022
PROG

(MAGMAMagma) [(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

Discussion
Thu Sep 08
08:44
OEIS Server: https://oeis.org/edit/global/2944
#20 by Harvey P. Dale at Sun May 20 17:41:29 EDT 2018
STATUS

editing

approved

#19 by Harvey P. Dale at Sun May 20 17:41:22 EDT 2018
MATHEMATICA

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 *)

STATUS

approved

editing

#18 by Alois P. Heinz at Sun Oct 08 17:40:31 EDT 2017
STATUS

proposed

approved

#17 by Jon E. Schoenfield at Sun Oct 08 17:28:14 EDT 2017
STATUS

editing

proposed

#16 by Jon E. Schoenfield at Sun Oct 08 17:28:11 EDT 2017
FORMULA

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

STATUS

proposed

editing

#15 by Michel Marcus at Sun Oct 08 17:02:07 EDT 2017
STATUS

editing

proposed

#14 by Michel Marcus at Sun Oct 08 17:02:03 EDT 2017
REFERENCES

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 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).

LINKS

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.

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.

STATUS

proposed

editing

#13 by G. C. Greubel at Sun Oct 08 14:18:02 EDT 2017
STATUS

editing

proposed

#12 by G. C. Greubel at Sun Oct 08 14:17:41 EDT 2017
LINKS

G. C. Greubel, <a href="/A052391/b052391.txt">Table of n, a(n) for n = 1..845</a>

<a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (71, -2205, 39495, -452523, 3473673, -18166175, 64427005, -150923976, 220549356, -178819920, 59875200).

FORMULA

a(n) = 1/4!*(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 *)

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

STATUS

approved

editing