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

1, 343, 6859, 50653, 226981, 753571, 2048383, 4826809, 10218313, 19902511, 36264691, 62570773, 103161709, 163667323, 251239591, 374805361, 545338513, 776151559, 1083206683, 1485446221, 2005142581, 2668267603, 3504881359, 4549540393, 5841725401, 7426288351

Offset: 0

Author

Indranil Ghosh, Jan 02 2017

Keywords

• nonn
• easy

Comments

a(n) is a perfect cube.

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

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

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

Cf. A003215.

Programs

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

Python

def a(n):
    return 27*n**6-81*n**5+108*n**4-81*n**3+36*n**2-9*n+1

Formula

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

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

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