A168555 a(n) = n^6*(n^3 + 1)/2.

0, 1, 288, 10206, 133120, 984375, 5062176, 20235628, 67239936, 193975965, 500500000, 1179859626, 2581383168, 5304663091, 10334288160, 19227375000, 34368126976, 59306007033, 99196651296, 161367371830, 256032000000, 397182906351, 603691298848, 900650348676

Offset

0,3

Comments

a(n) is the number of inequivalent 3 X 3 matrices with entries in {1,2,...,n} when a matrix and its transpose are considered equivalent. - Geoffrey Critzer, Dec 18 2011.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: x*(1 + 278*x + 7371*x^2 + 43900*x^3 + 78095*x^4 + 44334*x^5 + 7237*x^6 + 224*x^7) / (1 - x)^10. - Colin Barker, Feb 23 2017

Mathematica

Table[n^6*(n^3 + 1)/2, {n, 0, 25}] (* G. C. Greubel, Jul 26 2016 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 288, 10206, 133120, 984375, 5062176, 20235628, 67239936, 193975965}, 30] (* Harvey P. Dale, Apr 26 2024 *)

Prog

(Magma) [n^6*(n^3+1)/2: n in [0..30]]; // Vincenzo Librandi, Aug 29 2011
(PARI) a(n) = (n^6+n^9)/2 \\ Charles R Greathouse IV, Dec 20 2011
(PARI) concat(0, Vec(x*(1 + 278*x + 7371*x^2 + 43900*x^3 + 78095*x^4 + 44334*x^5 + 7237*x^6 + 224*x^7) / (1 - x)^10 + O(x^30))) \\ Colin Barker, Feb 23 2017

Crossrefs

Sequence in context: A264204 A202165 A264001 * A163731 A223293 A035749

Adjacent sequences: A168552 A168553 A168554 * A168556 A168557 A168558

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 2009

Status

approved