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A282613 Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to rotations. 13
0, 1, 140, 4995, 65824, 489125, 2521476, 10092775, 33562880, 96870249, 250025500, 589527851, 1290008160, 2651218765, 5165397524, 9611031375, 17180133376, 29647326545, 49590297900, 80672546899, 128000804000, 198571037301, 301818598180, 450289780535 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Cycle index of symmetry group (cyclic rotation group of order 4 acting on the 9 cells of the square) is (2s(4)^2*s(1) + s(2)^4*s(1) + s(1)^9)/4.
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
a(n) = n^3*(n^2+1)*(n^4-n^2+2)/4.
G.f.: x*(1 + 130*x + 3640*x^2 + 22054*x^3 + 39070*x^4 + 22054*x^5 + 3640*x^6 + 130*x^7 + x^8) / (1 - x)^10. - Colin Barker, Feb 23 2017
EXAMPLE
The number of 3 X 3 binary matrices up to rotations is 140.
MATHEMATICA
Table[(2n^3+n^5+n^9)/4, {n, 0, 24}]
PROG
(PARI) concat(0, Vec(x*(1 + 130*x + 3640*x^2 + 22054*x^3 + 39070*x^4 + 22054*x^5 + 3640*x^6 + 130*x^7 + x^8) / (1 - x)^10 + O(x^30))) \\ Colin Barker, Feb 23 2017
CROSSREFS
Row n=3 of A343095.
Cf. A006528 (2 x 2 version), A283027 (4 X 4 version).
Sequence in context: A128193 A061607 A223349 * A202786 A035820 A075915
KEYWORD
nonn,easy
AUTHOR
David Nacin, Feb 19 2017
STATUS
approved

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Last modified February 22 02:45 EST 2024. Contains 370239 sequences. (Running on oeis4.)