login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282612 Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to row permutations. 10
0, 1, 120, 3654, 45760, 333375, 1703016, 6784540, 22500864, 64836045, 167167000, 393877506, 861456960, 1769830699, 3447273480, 6412923000, 11461636096, 19776716505, 33076889784, 53804808190, 85365336000, 132422893911, 201268229800, 300266132244, 440396812800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Cycle index of symmetry group is (3*s(2)^3*s(1)^3 + 2*s(3)^3 + s(1)^9)/6.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

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^3+2)*(n+1)*(n^2-n+1)/6.

G.f.: x*(1 + 110*x + 2499*x^2 + 14500*x^3 + 26015*x^4 + 14934*x^5 + 2365*x^6 + 56*x^7) / (1 - x)^10. - Colin Barker, Feb 23 2017

EXAMPLE

The number of 3 X 3 binary matrices up to row permutations is 120.

MATHEMATICA

Table[(3n^6+2n^3+n^9)/6, {n, 0, 24}]

PROG

(PARI) concat(0, Vec(x*(1 + 110*x + 2499*x^2 + 14500*x^3 + 26015*x^4 + 14934*x^5 + 2365*x^6 + 56*x^7) / (1 - x)^10 + O(x^30))) \\ Colin Barker, Feb 23 2017

CROSSREFS

Cf. A282613, A282614, A217331, A168555. A037270 (2x2 version.)

Sequence in context: A183266 A231129 A052722 * A231136 A222003 A139389

Adjacent sequences:  A282609 A282610 A282611 * A282613 A282614 A282615

KEYWORD

nonn,easy

AUTHOR

David Nacin, Feb 19 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 29 04:32 EST 2020. Contains 332353 sequences. (Running on oeis4.)