|
%I #34 Jun 02 2023 09:06:29
%S 1,6,34,190,1053,5624,28576,136758,613894,2583164,10208743,38013716,
%T 133872584,447620002,1426354541,4346885204,12710830673,35768703586,
%U 97125981825,255111287298,649598148384,1606754306778,3867515638005,9074220508038,20784247213232
%N Number of 5 X n binary matrices up to row and column permutations.
%H Andrew Howroyd, <a href="/A052264/b052264.txt">Table of n, a(n) for n = 0..1000</a>
%H Vladeta Jovovic, <a href="/A005748/a005748.pdf">Binary matrices up to row and column permutations</a>
%H Míšek [Misek], Bohuslav: <a href="http://dml.cz/handle/10338.dmlcz/108444">O počtu tříd silně ekvivalentních incidenčních matic</a>. (Czech) [On the number of classes of strongly equivalent incidence matrices]. Časopis pro pěstování matematiky, vol. 89 (1964), issue 2, pp. 211-218.
%H <a href="/index/Rec#order_100">Index entries for linear recurrences with constant coefficients</a>, signature (8, -24, 30, -6, -18, 27, -60, 87, -108, 147, -36, -82, 8, -147, 260, -253, 672, -413, -14, -471, -270, 612, -330, 2024, -1042, 213, -2022, -423, -18, 600, 4032, -858, 1468, -4952, -714, -3255, 1722, 5577, 1638, 4032, -5862, -1352, -8594, 1530, 3114, 5619, 6306, -2324, -170, -11814, -170, -2324, 6306, 5619, 3114, 1530, -8594, -1352, -5862, 4032, 1638, 5577, 1722, -3255, -714, -4952, 1468, -858, 4032, 600, -18, -423, -2022, 213, -1042, 2024, -330, 612, -270, -471, -14, -413, 672, -253, 260, -147, 8, -82, -36, 147, -108, 87, -60, 27, -18, -6, 30, -24, 8, -1).
%F G.f.: (x^68 - 2*x^67 + 10*x^66 + 32*x^65 + 175*x^64 + 794*x^63 + 3441*x^62 + 13186*x^61 + 46027*x^60 + 146118*x^59 + 427347*x^58 + 1155432*x^57 + 2912873*x^56 + 6875608*x^55 + 15281029*x^54 + 32094658*x^53 + 63945531*x^52 + 121210914*x^51 + 219194198*x^50 + 378998758*x^49 + 627863648*x^48 + 998282344*x^47 + 1525746624*x^46 + 2244502676*x^45 + 3181886869*x^44 + 4351201210*x^43 + 5744918381*x^42 + 7328807372*x^41 + 9039504349*x^40 + 10785767638*x^39 + 12455264802*x^38 + 13925287384*x^37 + 15077477135*x^36 + 15812782150*x^35 + 16065602576*x^34 + 15812782150*x^33 + 15077477135*x^32 + 13925287384*x^31 + 12455264802*x^30 + 10785767638*x^29 + 9039504349*x^28 + 7328807372*x^27 + 5744918381*x^26 + 4351201210*x^25 + 3181886869*x^24 + 2244502676*x^23 + 1525746624*x^22 + 998282344*x^21 + 627863648*x^20 + 378998758*x^19 + 219194198*x^18 + 121210914*x^17 + 63945531*x^16 + 32094658*x^15 + 15281029*x^14 + 6875608*x^13 + 2912873*x^12 + 1155432*x^11 + 427347*x^10 + 146118*x^9 + 46027*x^8 + 13186*x^7 + 3441*x^6 + 794*x^5 + 175*x^4 + 32*x^3 + 10*x^2 - 2*x + 1)/((x^6 - 1)^2*(x^4 + x^3 + x^2 + x + 1)^6*(x^3 - x^2 + x - 1)^6 * (x^2 + x + 1)^6*(x + 1)^10*(x - 1)^24).
%o (PARI) Vec(G(5, x) + O(x^40)) \\ G defined in A028657. - _Andrew Howroyd_, Feb 28 2023
%Y Cf. A002623, A002727, A006148.
%Y A diagonal of the array A(m,n) described in A028657. - _N. J. A. Sloane_, Sep 01 2013
%K easy,nonn
%O 0,2
%A _Vladeta Jovovic_, Feb 04 2000
%E Name clarified by _Ching Pong Siu_, Aug 30 2022
|
