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A210370 Number of 2 X 2 matrices with all elements in {0,1,...,n} and odd determinant. 6
0, 6, 16, 96, 168, 486, 720, 1536, 2080, 3750, 4800, 7776, 9576, 14406, 17248, 24576, 28800, 39366, 45360, 60000, 68200, 87846, 98736, 124416, 138528, 171366, 189280, 230496, 252840 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) + A210369(n) = n^4.

a(n) is also the number of 2 X 2 matrices with all elements in {0,1,...n} and odd permanent.

LINKS

Table of n, a(n) for n=0..28.

FORMULA

Conjecture: a(n) = (3-3*(-1)^n-12*(-1+(-1)^n)*n+(22-14*(-1)^n)*n^2-4*(-5+(-1)^n)*n^3+6*n^4)/16. - Colin Barker, Nov 28 2014

Empirical g.f.: -2*x*(3*x^5+17*x^4+16*x^3+28*x^2+5*x+3) / ((x-1)^5*(x+1)^4). - Colin Barker, Nov 28 2014

MATHEMATICA

a = 0; b = n; z1 = 28;

t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]

c[n_, k_] := c[n, k] = Count[t[n], k]

u[n_] := Sum[c[n, 2 k], {k, -2*n^2, 2*n^2}]

v[n_] := Sum[c[n, 2 k - 1], {k, -2*n^2, 2*n^2}]

Table[u[n], {n, 0,  z1}] (* A210369 *)

Table[v[n], {n, 0, z1}](* A210370 *)

CROSSREFS

Cf. A210000.

Sequence in context: A009352 A056204 A091148 * A266180 A229566 A222965

Adjacent sequences:  A210367 A210368 A210369 * A210371 A210372 A210373

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved

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Last modified February 21 04:18 EST 2019. Contains 320371 sequences. (Running on oeis4.)