A211056 - OEIS

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A211056

Number of 2 X 2 nonsingular matrices having all terms in {1,...,n}.

0, 10, 66, 224, 576, 1210, 2290, 3936, 6352, 9722, 14322, 20304, 28080, 37834, 49922, 64704, 82624, 103898, 129170, 158640, 192944, 232554, 278050, 329680, 388368, 454522, 528770, 611680, 704192, 806490, 919890, 1044624, 1181680

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OFFSET

1,2

COMMENTS

A211056(n) + A134506(n) = n^4.

For a guide to related sequences, see A210000.

LINKS

Table of n, a(n) for n=1..33.

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] - c[n, 0], {n, 1, z1}] (* A211059 *)

2*% (* A211056 *)

CROSSREFS

Cf. A134506, A210000, A211059.

Sequence in context: A140362 A159838 A269679 * A269468 A024391 A074362

Adjacent sequences: A211053 A211054 A211055 * A211057 A211058 A211059

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 31 2012

STATUS

approved