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A211058
Number of 2 X 2 matrices having all terms in {1,...,n} and nonnegative determinant.
3
1, 11, 48, 144, 337, 691, 1256, 2128, 3385, 5139, 7480, 10584, 14521, 19499, 25664, 33184, 42209, 53027, 65736, 80680, 98009, 117979, 140816, 166936, 196441, 229715, 267056, 308816, 355185, 406755, 463576, 526264, 595081, 670419
OFFSET
1,2
COMMENTS
For a guide to related sequences, see A210000.
LINKS
MAPLE
g:= proc(n) local T, a, b, t, i, r;
T:= Vector(n^2):
for a from 1 to n do T[a^2]:= 1 od:
for a from 1 to n-1 do for b from a+1 to n do
T[a*b]:= T[a*b]+2
od od;
r:= n^2;
t:= T[1]*r;
for i from 2 to n^2 do
r:= r - T[i-1];
t:= t + T[i]*r;
od;
t
end proc:
g(1):= 1:
map(g, [$1..40]); # Robert Israel, Sep 06 2024
MATHEMATICA
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]
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]
Table[c1[n, n^2], {n, 1, z1}] (* A211058 *)
CROSSREFS
Cf. A210000.
Sequence in context: A042984 A364579 A008780 * A239460 A226676 A101992
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 31 2012
STATUS
approved