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A210372 Number of 2 X 2 matrices with all elements in {0,1,...,n} and positive even determinant. 4
0, 0, 17, 48, 172, 320, 713, 1112, 2016, 2840, 4561, 6056, 8964, 11400, 15977, 19648, 26400, 31744, 41257, 48664, 61620, 71512, 88689, 101680, 123800, 140376, 168449, 189232, 224108, 249840, 292545 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

See A210000 for a guide to related sequences.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = (A210369(n) - A059306(n))/2. - Chai Wah Wu, Nov 27 2016

MATHEMATICA

a = 0; b = n; z1 = 30;

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_] := u[n] = Sum[c[n, 2 k], {k, 0, n^2}]

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

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

Table[u[n], {n, 0, z1}] (* A210371 *)

Table[v[n], {n, 0, z1}] (* A210372 *)

Table[w[n], {n, 0, z1}] (* A210373 *)

CROSSREFS

Cf. A210000.

Sequence in context: A051869 A297818 A297988 * A239130 A181426 A029487

Adjacent sequences:  A210369 A210370 A210371 * A210373 A210374 A210375

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 20 2012

EXTENSIONS

Offset corrected by Chai Wah Wu, Nov 27 2016

STATUS

approved

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Last modified March 18 22:11 EDT 2019. Contains 321305 sequences. (Running on oeis4.)