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A210290
Number of 2 X 2 matrices with all elements in {0,1,...,n} and nonnegative determinant.
2
1, 13, 56, 160, 369, 733, 1328, 2216, 3505, 5285, 7680, 10792, 14809, 19813, 26024, 33600, 42721, 53549, 66384, 81336, 98761, 118821, 141784, 167888, 197561, 230917, 268352, 310176, 356753, 408285, 465376, 528088, 597049, 672533, 754944, 844744, 942425
OFFSET
0,2
COMMENTS
See A210000 for a guide to related sequences.
LINKS
FORMULA
a(n) = ((n+1)^4 + A059306(n))/2. - Andrew Howroyd, Apr 28 2020
MATHEMATICA
a = 0; b = n; z1 = 45;
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]
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]
Table[c1[n, n^2], {n, 0, z1}] (* A210290 *)
CROSSREFS
Sequence in context: A061161 A212053 A264853 * A007202 A368813 A222161
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 19 2012
EXTENSIONS
Terms a(34) and beyond from Andrew Howroyd, Apr 28 2020
STATUS
approved