A052264 Number of 5 X n binary matrices up to row and column permutations.
1, 6, 34, 190, 1053, 5624, 28576, 136758, 613894, 2583164, 10208743, 38013716, 133872584, 447620002, 1426354541, 4346885204, 12710830673, 35768703586, 97125981825, 255111287298, 649598148384, 1606754306778, 3867515638005, 9074220508038, 20784247213232
Offset: 0
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1000
- Vladeta Jovovic, Binary matrices up to row and column permutations
- Míšek [Misek], Bohuslav: O počtu tříd silně ekvivalentních incidenčních matic. (Czech) [On the number of classes of strongly equivalent incidence matrices]. Časopis pro pěstování matematiky, vol. 89 (1964), issue 2, pp. 211-218.
- Index entries for linear recurrences with constant coefficients, 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).
Crossrefs
A diagonal of the array A(m,n) described in A028657. - N. J. A. Sloane, Sep 01 2013
Programs
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PARI
Vec(G(5, x) + O(x^40)) \\ G defined in A028657. - Andrew Howroyd, Feb 28 2023
Formula
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).
Extensions
Name clarified by Ching Pong Siu, Aug 30 2022