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A277636 Number of 3 X 3 matrices having all elements in {0,...,n} with determinant = permanent. 1

%I #34 Jan 02 2017 20:35:22

%S 1,343,6859,50653,226981,753571,2048383,4826809,10218313,19902511,

%T 36264691,62570773,103161709,163667323,251239591,374805361,545338513,

%U 776151559,1083206683,1485446221,2005142581,2668267603,3504881359,4549540393,5841725401,7426288351

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

%C a(n) is a perfect cube.

%H Indranil Ghosh, <a href="/A277636/b277636.txt">Table of n, a(n) for n = 0..100</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F a(n) = A003215(n-1)^3.

%F a(n) = (3*n^2 - 3*n + 1)^3.

%F 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 (Python)

%o def a(n):

%o return 27*n**6-81*n**5+108*n**4-81*n**3+36*n**2-9*n+1

%o (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 Cf. A059976 (Number of 3 X 3 singular matrices with all elements in {0,...,n})

%Y Cf. A015237 (Number of 2 X 2 matrices with all elements in {0,...,n} with determinant = permanent )

%Y Cf. A003215.

%K nonn,easy

%O 0,2

%A _Indranil Ghosh_, Jan 02 2017

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Last modified March 29 09:32 EDT 2024. Contains 371268 sequences. (Running on oeis4.)