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Number of n X 5 binary matrices under row and column permutations and column complementations.
3

%I #10 Jun 02 2023 11:43:50

%S 1,1,6,16,81,299,1358,5567,23350,91998,351058,1269907,4394634,

%T 14495236,45779246,138567568,403282017,1130773069,3062535192,

%U 8028046724,20411824364,50429813556,121280243676,284360432241,650972702410

%N Number of n X 5 binary matrices under row and column permutations and column complementations.

%D M. A. Harrison, On the number of classes of binary matrices, IEEE Trans. Computers, 22 (1973), 1048-1051.

%H Andrew Howroyd, <a href="/A056204/b056204.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_148">Index entries for linear recurrences with constant coefficients</a>, order 148.

%F G.f.: 1/3840*(1/(1 - x^1)^32 + 231/(1 - x^2)^16 + 20/(1 - x^1)^16/(1 - x^2)^8 + 520/(1 - x^4)^8 + 60/(1 - x^1)^8/(1 - x^2)^12 + 80/(1 - x^1)^8/(1 - x^3)^8 + 720/(1 - x^2)^4/(1 - x^6)^4 + 160/(1 - x^1)^4/(1 - x^2)^2/(1 - x^3)^4/(1 - x^6)^2 + 320/(1 - x^4)^2/(1 - x^12)^2 + 240/(1 - x^1)^4/(1 - x^2)^2/(1 - x^4)^6 + 480/(1 - x^8)^4 + 240/(1 - x^2)^4/(1 - x^4)^6 + 384/(1 - x^1)^2/(1 - x^5)^6 + 384/(1 - x^2)^1/(1 - x^10)^3).

%Y Column k=5 of A363349.

%Y Cf. A005232, A006380, A006381, A006382, A002727, A006148, A052264.

%K nonn

%O 0,3

%A _Vladeta Jovovic_, Aug 05 2000