cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

A051180 Number of 3-element intersecting families of an n-element set.

Original entry on oeis.org

0, 0, 0, 13, 222, 2585, 25830, 238833, 2111382, 18142585, 152937510, 1271964353, 10476007542, 85662034185, 696700867590, 5643519669073, 45575393343702, 367206720319385, 2953481502692070, 23723872215168993, 190372457332919862
Offset: 0

Views

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

Links

Crossrefs

Cf. A036239, A051181-A051185.

Programs

  • Maple
    seq(1/3!*(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2),n=0..40);
  • Mathematica
    Table[1/3!(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2),{n,0,30}] (* or *) LinearRecurrence[{29,-343,2135,-7504,14756,-14832,5760},{0,0,0,13,222,2585,25830},30] (* Harvey P. Dale, Jul 07 2013 *)
  • PARI
    for(n=0,25, print1((1/3!)*(8^n-3*6^n+3*5^n-4*4^n+3*3^n+2*2^n-2), ", ")) \\ G. C. Greubel, Oct 06 2017

Formula

a(n) = (1/3!)*(8^n - 3*6^n + 3*5^n - 4*4^n + 3*3^n + 2*2^n - 2).
G.f. x^3*(744*x^3 - 606*x^2 + 155*x - 13)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - Colin Barker, Jul 29 2012
a(0)=0, a(1)=0, a(2)=0, a(3)=13, a(4)=222, a(5)=2585, a(6)=25830, a(n) = 29*a(n-1) - 343*a(n-2) + 2135*a(n-3) - 7504*a(n-4) + 14756*a(n-5) - 14832*a(n-6) + 5760*a(n-7). - Harvey P. Dale, Jul 07 2013

Extensions

More terms from Sascha Kurz, Mar 25 2002

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

Views

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

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

Crossrefs

Cf. A036239, A051180, A051181, A051182, A051183, A051184, A051185.

Formula

a(n) = (1/6!)*(64^n -20*56^n +90*52^n +30*50^n +25*49^n -420*48^n -180*47^n +450*46^n +60*45^n +615*44^n +1683*43^n -3252*42^n -6030*41^n +8520*40^n +10560*39^n -15849*38^n -13005*37^n +26410*36^n +10655*35^n -50385*34^n +33390*33^n +29480*32^n -82010*31^n +91215*30^n -67380*29^n +36870*28^n -15249*27^n +4380*26^n -1215*25^n +1390*24^n -695*23^n -1574*22^n +3255*21^n -3075*20^n +1800*19^n -675*18^n +150*17^n +70*16^n -340*14^n +510*13^n -340*12^n +85*11^n -225*8^n +225*7^n +274*4^n -274*3^n -120*2^n +120).

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

Views

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

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

Crossrefs

Cf. A036239, A051180, A051181, A051182, A051183, A051184, A051185.

Programs

  • Mathematica
    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 *)

Formula

a(n) = (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).

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

Views

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

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

Crossrefs

Cf. A036239, A051180, A051181, A051182, A051183, A051184, A051185.

Programs

  • Magma
    [(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
  • Mathematica
    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 *)
  • PARI
    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

Formula

a(n) = (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).
G.f.: -x^3*(47062848*x^7 -42816008*x^6 +13976678*x^5 -2170583*x^4 +168932*x^3 -5672*x^2 +2*x +3) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(7*x -1)*(8*x -1)*(11*x -1)*(12*x -1)*(13*x -1)*(14*x -1)*(16*x -1)). - Colin Barker, Jul 12 2013

Extensions

More terms from Colin Barker, Jul 12 2013

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

Views

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

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

Crossrefs

Cf. A036239, A051180, A051181, A051182, A051183, A051184, A051185.

Programs

  • Mathematica
    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 *)

Formula

a(n) = (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).

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

Views

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

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

Crossrefs

Cf. A036239, A051180, A051181, A051182, A051183, A051184, A051185.

Programs

  • Magma
    [(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
  • Mathematica
    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 *)
  • PARI
    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

Formula

a(n) = (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).

A052389 Number of 4-element intersecting families (with not necessarily distinct sets) of an n-element set.

Original entry on oeis.org

0, 1, 9, 95, 1286, 20681, 360964, 6452825, 114920766, 2018035121, 34864971944, 593281456505, 9965368457746, 165615181710161, 2728984827320124, 44665923097267385, 727216852411490726, 11791672548220250801
Offset: 0

Views

Author

Vladeta Jovovic, Goran Kilibarda, Mar 11 2000

Keywords

Links

Crossrefs

Cf. A051181, A053154, A053155.

Programs

  • Magma
    [(16^n - 6*12^n + 12*10^n - 9^n-10*8^n + 15*7^n - 24*6^n + 19*5^n + 5*4^n - 11*3^n + 6*2^n - 6)/24: n in [0..50]]; // G. C. Greubel, Oct 08 2017
  • Mathematica
    Table[(16^n - 6*12^n + 12*10^n - 9^n-10*8^n + 15*7^n - 24*6^n + 19*5^n + 5*4^n - 11*3^n + 6*2^n - 6)/24, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *)
  • PARI
    for(n=0,50, print1((16^n - 6*12^n + 12*10^n - 9^n-10*8^n + 15*7^n - 24*6^n + 19*5^n + 5*4^n - 11*3^n + 6*2^n - 6)/24, ", ")) \\ G. C. Greubel, Oct 08 2017

Formula

a(n) = (16^n - 6*12^n + 12*10^n - 9^n-10*8^n + 15*7^n - 24*6^n + 19*5^n + 5*4^n - 11*3^n + 6*2^n - 6)/24.
G.f.: x * (118224000*x^10 - 215558352*x^9 + 171543508*x^8 - 77761264*x^7 + 22230235*x^6 - 4199119*x^5 + 532266*x^4 - 44801*x^3 + 2400*x^2 - 74*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) * (10*x-1) * (12*x-1) * (16*x-1) ). - Colin Barker, Jul 30 2012

A052390 Number of 4-element intersecting families (with not necessarily distinct sets) whose union is an n-element set.

Original entry on oeis.org

1, 7, 71, 956, 15116, 254397, 4318511, 72331966, 1188180386, 19152566087, 303768582701, 4755204310776, 73675434833456, 1132450098258577, 17301032324486891, 263098797953058386, 3987051131522775326
Offset: 1

Views

Author

Vladeta Jovovic, Goran Kilibarda, Mar 11 2000

Keywords

Links

Crossrefs

Cf. A051181, A053156, A053157.

Programs

  • 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
  • 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

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

Original entry on oeis.org

0, 0, 4, 349, 9985, 213230, 4000444, 69940479, 1170549895, 19024433560, 302846958634, 4748624978009, 73628721516805, 1132119741733890, 17298702716660824, 263082403948681939, 3986935934969727715
Offset: 1

Views

Author

Vladeta Jovovic, Goran Kilibarda, Mar 11 2000

Keywords

Links

Crossrefs

Cf. A051181, A053152, A053153.

Programs

  • 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
  • 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 *)
  • 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

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

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

Views

Author

Vladeta Jovovic, Goran Kilibarda

Keywords

References

  • 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).

Links

Formula

A051184(n)-A051183(n)+A051182(n)-A051181(n)+A051180(n)-A036239(n)+A000918(n)
Showing 1-10 of 10 results.

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