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A051589 Number of 5xn binary matrices such that any 2 rows have a common 1. 5
0, 1, 63, 3367, 167835, 7803391, 339133803, 13887495007, 541044196875, 20237096702431, 732455240043243, 25820836854042847, 891331324715015115, 30260208833985800671, 1013882831306569043883, 33620617443978687281887, 1105857774681062127612555 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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.

FORMULA

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]

MATHEMATICA

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 *)

PROG

(MAGMA) [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

CROSSREFS

Cf. A005061, A051588, A051587.

Sequence in context: A167987 A273437 A069381 * A203457 A258684 A180926

Adjacent sequences:  A051586 A051587 A051588 * A051590 A051591 A051592

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Goran Kilibarda. Revised Aug 03 2000.

STATUS

approved

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Last modified June 17 15:28 EDT 2019. Contains 324194 sequences. (Running on oeis4.)