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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 11 2009
STATUS
approved