A051587 -id:A051587 - cp's OEIS frontend

A051589 Number of 5xn binary matrices such that any 2 rows have a common 1.

0, 1, 63, 3367, 167835, 7803391, 339133803, 13887495007, 541044196875, 20237096702431, 732455240043243, 25820836854042847, 891331324715015115, 30260208833985800671, 1013882831306569043883, 33620617443978687281887, 1105857774681062127612555

Offset: 0

Vladeta Jovovic, Goran Kilibarda

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..670
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.

Cf. A005061, A051587, A051588.

List([0..20], n-> 32^n-10*24^n+30*20^n-5*18^n+5*17^n-70*16^n-30*15^n +135*14^n +30*13^n-140*12^n-2*11^n+130*10^n-110*9^n+45*8^n-10*7^n +6^n); # G. C. Greubel, Nov 12 2019

[32^n-10*24^n+30*20^n-5*18^n+5*17^n-70*16^n-30*15^n +135*14^n +30*13^n-140*12^n-2*11^n+130*10^n-110*9^n+45*8^n-10*7^n +6^n: n in [0..20]]; // Vincenzo Librandi, Sep 18 2018

A051589(n):=32^n -10*24^n +30*20^n -5*18^n +5*17^n -70*16^n -30*15^n + 135*14^n +30*13^n -140*12^n -2*11^n +130*10^n -110*9^n +45*8^n -10*7^n +6^n; seq(A051589(n), n=0..20); # G. C. Greubel, Nov 12 2019

Table[32^n -10*24^n +30*20^n -5*18^n +5*17^n -70*16^n -30*15^n +135*14^n +30*13^n -140*12^n -2*11^n +130*10^n -110*9^n +45*8^n -10*7^n +6^n, {n, 0, 30}] (* Vincenzo Librandi, Sep 18 2018 *)

vector(21, n, m=n-1; 32^m -10*24^m +30*20^m -5*18^m +5*17^m -70*16^m -30*15^m +135*14^m +30*13^m -140*12^m -2*11^m +130*10^m -110*9^m +45*8^m -10*7^m +6^m) \\ G. C. Greubel, Nov 12 2019

[32^n-10*24^n+30*20^n-5*18^n+5*17^n-70*16^n-30*15^n +135*14^n +30*13^n-140*12^n-2*11^n+130*10^n-110*9^n+45*8^n-10*7^n +6^n for n in (0..20)] # G. C. Greubel, Nov 12 2019

a(n) = 32^n - 10*24^n + 30*20^n - 5*18^n + 5*17^n - 70*16^n - 30*15^n + 135*14^n + 30*13^n - 140*12^n - 2*11^n + 130*10^n - 110*9^n + 45*8^n - 10*7^n + 6^n.

G.f.: x*(933561925632000*x^14 -1286309121638400*x^13 +786606914672640*x^12 -287219252934144*x^11 +70324589076096*x^10 -12248067009984*x^9 +1568017231256*x^8 -150181430252*x^7 +10834851518*x^6 -587198697*x^5 +23594853*x^4 -684354*x^3 +13636*x^2 -169*x +1) / ((6*x -1)*(7*x -1)*(8*x -1)*(9*x -1)*(10*x -1)*(11*x -1)*(12*x -1)*(13*x -1)*(14*x -1)*(15*x -1)*(16*x -1)*(17*x -1)*(18*x -1)*(20*x -1)*(24*x -1)*(32*x -1)). - Colin Barker, Feb 22 2013

Revised Aug 03 2000

A052387 Number of 3 X n binary matrices such that any 2 rows have a common 1, up to column permutations.

Original entry on oeis.org

0, 1, 8, 37, 127, 358, 876, 1926, 3894, 7359, 13156, 22451, 36829, 58396, 89896, 134844, 197676, 283917, 400368, 555313, 758747, 1022626, 1361140, 1791010, 2331810, 3006315, 3840876, 4865823, 6115897, 7630712, 9455248

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Mar 11 2000

G. C. Greubel, Table of n, a(n) for n = 0..1000
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).
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A051588, A051587, A051589.

[n*(n+1)*(n+2)*(n+3)*(n^3+22*n^2+53*n+134)/5040: n in [0..30]]; // Wesley Ivan Hurt, May 15 2014

A052387:=n->n*(n+1)*(n+2)*(n+3)*(n^3+22*n^2+53*n+134)/5040; seq(A052387(n), n=0..30); # Wesley Ivan Hurt, May 15 2014

Table[n*(n + 1)*(n + 2)*(n + 3)*(n^3 + 22*n^2 + 53*n + 134)/5040, {n,
0, 30}] (* Wesley Ivan Hurt, May 15 2014 *)

x='x+O('x^50); concat([0], Vec(-x*(x^3-x^2-1)/(x-1)^8)) \\ G. C. Greubel, Oct 07 2017

a(n) = n*(n+1)*(n+2)*(n+3)*(n^3 +22*n^2 +53*n +134)/5040.

G.f.: -x*(x^3-x^2-1)/(x-1)^8. - Colin Barker, Nov 05 2012

A052388 Number of 4 X n binary matrices such that any 2 rows have a common 1, up to column permutations.

Original entry on oeis.org

0, 1, 16, 146, 955, 4905, 20907, 76851, 250530, 739612, 2009177, 5085119, 12109526, 27348478, 58955082, 121956402, 243172488, 469115187, 878387366, 1600751976, 2845918041, 4946262815, 8419256605, 14057377245, 23055913530, 37192403430, 59075703351, 92488040301

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Mar 11 2000

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).

T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Cf. A051588, A051587, A051589.

[n*(n+1)*(n+2)*(n+3)*(n+4)*(n^10 +110*n^9 +5445*n^8 +160050*n^7 +2906463*n^6 +30644250*n^5 +176659055*n^4 +711220750*n^3 +1781493036*n^2 +4034382840*n +4159814400)/1307674368000: n in [0..25]]; // G. C. Greubel, Oct 07 2017

CoefficientList[Series[-x*(x^10 -5*x^9 +10*x^8 -14*x^7 +21*x^6 -19*x^5 -5*x^4 +21*x^3 -10*x^2 -1)/(x-1)^16, {x, 0, 50}], x] (* G. C. Greubel, Oct 07 2017 *)

x='x+O('x^50); concat([0], Vec(-x*(x^10 -5*x^9 +10*x^8 -14*x^7 +21*x^6 -19*x^5 -5*x^4 +21*x^3 -10*x^2 -1)/(x-1)^16)) \\ G. C. Greubel, Oct 07 2017

a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n^10 +110*n^9 +5445*n^8 +160050*n^7 +2906463*n^6 +30644250*n^5 +176659055*n^4 +711220750*n^3 +1781493036*n^2 +4034382840*n +4159814400)/1307674368000.

G.f.: -x*(x^10 -5*x^9 +10*x^8 -14*x^7 +21*x^6 -19*x^5 -5*x^4 +21*x^3 -10*x^2 -1)/(x-1)^16. - Colin Barker, Nov 05 2012

A319366 Number of 6 X n binary matrices such that any 2 rows have a common 1.

Original entry on oeis.org

1, 127, 14197, 1527655, 154708741, 14581420567, 1282928605477, 106281575400295, 8370106554738181, 632240233746846007, 46159332156459328357, 3278558540783856976135, 227767526682511220042821, 15545657368091391819871447, 1046175606578621216182684837

Offset: 1

T. V. Raziman, Sep 17 2018

nonn

Mathematics Stack Exchange, An interesting combinatorics problem
Quora, How many ways are there to set N people into M groups so that every two groups have at least one common member?

Cf. A051587, A051588, A051589.

a(n) = 64^n - 15*48^n + 60*40^n - 15*36^n + 30*34^n - 6*33^n - 200*32^n - 180*30^n + 585*28^n + 45*27^n + 60*26^n + 150*25^n - 660*24^n - 360*23^n + 168*22^n - 585*21^n + 1245*20^n + 1665*19^n - 1965*18^n - 2100*17^n + 2170*16^n + 1325*15^n - 1770*14^n - 420*13^n + 1533*12^n - 1105*11^n + 435*10^n - 105*9^n + 15*8^n - 7^n (proved in the Quora answer).

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A051589 Number of 5xn binary matrices such that any 2 rows have a common 1.

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A052387 Number of 3 X n binary matrices such that any 2 rows have a common 1, up to column permutations.

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A052388 Number of 4 X n binary matrices such that any 2 rows have a common 1, up to column permutations.

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A319366 Number of 6 X n binary matrices such that any 2 rows have a common 1.

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