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A211065
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Number of 2 X 2 matrices having all terms in {1,...,n} and odd determinant.
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4
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0, 6, 40, 96, 288, 486, 1056, 1536, 2800, 3750, 6120, 7776, 11760, 14406, 20608, 24576, 33696, 39366, 52200, 60000, 77440, 87846, 110880, 124416, 154128, 171366, 208936, 230496, 277200, 303750, 360960, 393216, 462400, 501126, 583848
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OFFSET
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1,2
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COMMENTS
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For a guide to related sequences, see A210000.
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LINKS
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FORMULA
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a(n) = (2*n + 1 -(-1)^n)^2*(6*n + 1 -(-1)^n)*(2*n - 1 + (-1)^n)/128.
a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 6*a(n-4) + 6*a(n-5) + 4*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9) for n > 9.
G.f.: -2*x^2*(3*x^5 + 5*x^4 + 28*x^3 + 16*x^2 + 17*x + 3)/((x - 1)^5*(x + 1)^4).
(End)
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MATHEMATICA
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a = 1; b = n; z1 = 35;
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, 1, z1}] (* A211064 *)
Table[v[n], {n, 1, z1}] (* A211065 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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