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A277636 Number of 3 X 3 matrices having all elements in {0,...,n} with determinant = permanent.

%I A277636 #34 Jan 02 2017 20:35:22
%S A277636 1,343,6859,50653,226981,753571,2048383,4826809,10218313,19902511,
%T A277636 36264691,62570773,103161709,163667323,251239591,374805361,545338513,
%U A277636 776151559,1083206683,1485446221,2005142581,2668267603,3504881359,4549540393,5841725401,7426288351
%N A277636 Number of 3 X 3 matrices having all elements in {0,...,n} with determinant = permanent.
%C A277636 a(n) is a perfect cube.
%H A277636 Indranil Ghosh, <a href="/A277636/b277636.txt">Table of n, a(n) for n = 0..100</a>
%H A277636 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A277636 a(n) = A003215(n-1)^3.
%F A277636 a(n) = (3*n^2 - 3*n + 1)^3.
%F A277636 G.f.: (1 + 336*x + 4479*x^2 + 9808*x^3 + 4479*x^4 + 336*x^5 + x^6) / (1 - x)^7. - _Colin Barker_, Jan 02 2017
%o A277636 (Python)
%o A277636 def a(n):
%o A277636     return 27*n**6-81*n**5+108*n**4-81*n**3+36*n**2-9*n+1
%o A277636 (PARI) Vec((1 + 336*x + 4479*x^2 + 9808*x^3 + 4479*x^4 + 336*x^5 + x^6) / (1 - x)^7 + O(x^30)) \\ _Colin Barker_, Jan 02 2017
%Y A277636 Cf. A059976 (Number of 3 X 3 singular matrices with all elements in {0,...,n})
%Y A277636 Cf. A015237 (Number of 2 X 2 matrices with all elements in {0,...,n} with determinant = permanent )
%Y A277636 Cf. A003215.
%K A277636 nonn,easy
%O A277636 0,2
%A A277636 _Indranil Ghosh_, Jan 02 2017