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A283026
Number of inequivalent 4 X 4 matrices with entries in {1,2,3,..,n} up to row permutations.
7
0, 1, 3876, 1929501, 183181376, 6419043125, 118091211876, 1388168405001, 11745311589376, 77279801651001, 416916712502500, 1915356782994501, 7705740009485376, 27731516944463501, 90762229896563876, 273716119247180625, 768684707117285376, 2027695320242670001
OFFSET
0,3
COMMENTS
Cycle index of symmetry group S4 acting on the 16 entries is (6*s(2)^4s(1)^8 + 8*s(3)^4s(1)^4 + 3*s(2)^8 + 6*s(4)^4 + s(1)^{16})/24.
FORMULA
a(n) = n^4*(n^4 + 1)*(n^4 + 2)*(n^4 + 3)/24.
From Chai Wah Wu, Dec 07 2018: (Start)
a(n) = 17*a(n-1) - 136*a(n-2) + 680*a(n-3) - 2380*a(n-4) + 6188*a(n-5) - 12376*a(n-6) + 19448*a(n-7) - 24310*a(n-8) + 24310*a(n-9) - 19448*a(n-10) + 12376*a(n-11) - 6188*a(n-12) + 2380*a(n-13) - 680*a(n-14) + 136*a(n-15) - 17*a(n-16) + a(n-17) for n > 16.
G.f.: -x*(x + 1)*(x^14 + 3858*x^13 + 1859887*x^12 + 149046428*x^11 + 3415692141*x^10 + 29161611758*x^9 + 104450960739*x^8 + 161533106376*x^7 + 104450960739*x^6 + 29161611758*x^5 + 3415692141*x^4 + 149046428*x^3 + 1859887*x^2 + 3858*x + 1)/(x - 1)^17. (End)
EXAMPLE
For n=2 we get a(2)=3876 inequivalent 4x4 binary matrices up to row permutations.
MATHEMATICA
Table[n^4*(n^4 + 1)*(n^4 + 2)*(n^4 + 3)/24, {n, 0, 30}]
PROG
(PARI) a(n) = n^4*(n^4 + 1)*(n^4 + 2)*(n^4 + 3)/24; \\ Indranil Ghosh, Feb 27 2017
(Python) def A283026(n) : return n**4*(n**4 + 1)*(n**4 + 2)*(n**4 + 3)/24 # Indranil Ghosh, Feb 27 2017
CROSSREFS
Cf. A282613, A282614, A283027, A283028, A283029, A283031, A283032, A283033. A283030 (5x5 version). A282612 (3x3 version). A037270 (2x2 version).
Sequence in context: A108005 A065696 A246735 * A014891 A253484 A253479
KEYWORD
easy,nonn
AUTHOR
David Nacin, Feb 27 2017
STATUS
approved