A051363
Number of 6-element families of an n-element set such that every 3 members of the family have a nonempty intersection.
Original entry on oeis.org
0, 0, 0, 0, 112, 40286, 5485032, 534844548, 45066853496, 3538771308282, 267882021563464, 19861835713621616, 1453175611052688600, 105278656040052332838, 7564280930105061931496, 539399446172552069053404
Offset: 0
- 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).
A051364
Number of 5-element families of an n-element set such that every 3 members of the family have a nonempty intersection.
Original entry on oeis.org
0, 0, 0, 0, 225, 21571, 1174122, 51441824, 2038356243, 76714338477, 2804947403364, 100732231517698, 3572491367063421, 125474030774355263, 4371052010746528926, 151172238539268318372
Offset: 0
- 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).
-
Table[1/5! (32^n - 10*28^n + 30*26^n + 5*25^n - 80*24^n + 45*23^n + 105*22^n - 217*21^n + 205*20^n - 120*19^n + 45*18^n - 10*17^n - 9*16^n + 40*14^n - 60*13^n + 40*12^n - 10*11^n + 35*8^n - 35*7^n - 50*4^n + 50*3^n + 24*2^n - 24), {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
A051365
Number of 4-element families of an n-element set such that every 3 members of the family have a nonempty intersection.
Original entry on oeis.org
0, 0, 0, 3, 275, 8475, 192385, 3831093, 71466675, 1285857975, 22632300245, 392522268633, 6734698919575, 114576024346875, 1935649374363705, 32505459713369373, 543014736097852475, 9029329231317194175, 149522990698790644765, 2466942184607949641313
Offset: 0
- 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).
-
[(16^n - 4*14^n + 6*13^n - 4*12^n + 11^n - 6*8^n + 6*7^n + 11*4^n - 11*3^n - 6*2^n + 6)/24: n in [0..50]]; // G. C. Greubel, Oct 08 2017
-
Table[1/4! (16^n - 4*14^n + 6*13^n - 4*12^n + 11^n - 6*8^n + 6*7^n + 11*4^n - 11*3^n - 6*2^n + 6), {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
-
for(n=0,50, print1((16^n - 4*14^n + 6*13^n - 4*12^n + 11^n - 6*8^n + 6*7^n + 11*4^n - 11*3^n - 6*2^n + 6)/24, ", ")) \\ G. C. Greubel, Oct 08 2017
A051366
Number of 6-element families of an n-element set such that every 4 members of the family have a nonempty intersection.
Original entry on oeis.org
0, 0, 0, 0, 112, 39761, 5318420, 506289623, 41378309308, 3133123494417, 227657567966500, 16152548751321851, 1129224692910819164, 78169242144478858373, 5373159786842137703140, 367368738925063893430959
Offset: 0
- 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).
-
Table[1/6! (64^n - 15*60^n + 60*58^n + 25*57^n - 240*56^n + 45*55^n + 705*54^n - 987*53^n - 351*52^n + 3040*51^n - 5445*50^n + 6105*49^n - 4939*48^n + 2997*47^n - 1365*46^n + 455*45^n - 105*44^n + 15*43^n - 42^n - 15*32^n + 75*30^n - 150*29^n + 150*28^n - 75*27^n + 15*26^n + 85*16^n - 85*15^n - 225*8^n + 225*7^n + 274*4^n - 274*3^n - 120*2^n + 120), {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
A051367
Number of 5-element families of an n-element set such that every 4 members of the family have a nonempty intersection.
Original entry on oeis.org
0, 0, 0, 0, 224, 21281, 1144027, 49310674, 1915317642, 70460566827, 2513684751809, 88008877380908, 3043421159408080, 104321464544910613, 3552122530256316471, 120307381384305672102
Offset: 0
- 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).
-
[(32^n - 5*30^n + 10*29^n - 10*28^n + 5*27^n - 26^n - 10*16^n + 10*15^n + 35*8^n - 35*7^n - 50*4^n + 50*3^n + 24*2^n - 24)/120: n in [0..50]]; // G. C. Greubel, Oct 08 2017
-
Table[(1/5!)*(32^n - 5*30^n + 10*29^n - 10*28^n + 5*27^n - 26^n - 10*16^n + 10*15^n + 35*8^n - 35*7^n - 50*4^n + 50*3^n + 24*2^n - 24), {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
-
for(n=0,50, print1((1/5!)*(32^n - 5*30^n + 10*29^n - 10*28^n + 5*27^n - 26^n - 10*16^n + 10*15^n + 35*8^n - 35*7^n - 50*4^n + 50*3^n + 24*2^n - 24), ", ")) \\ G. C. Greubel, Oct 08 2017
A051368
Number of Boolean functions of n variables and rank 8 from the Post class F(5,2).
Original entry on oeis.org
0, 0, 0, 12, 105765, 59046810, 16636450912, 3491313542424, 627725748292995, 102894277877828670, 15867914519581210614, 2343602605748557069356, 335205287948366997151705, 46782266953279485879549090
Offset: 1
- E. Post, Two-valued iterative systems, Annals of Mathematics, no 5, Princeton University Press, NY, 1941.
- 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).
Showing 1-6 of 6 results.