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

0,3

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

Maple

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

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
(PARI) 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
(Sage) [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
(GAP) 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

Crossrefs

Cf. A005061, A051587, A051588.

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