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A211064 Number of 2 X 2 matrices having all terms in {1,...,n} and even determinant. 5
1, 10, 41, 160, 337, 810, 1345, 2560, 3761, 6250, 8521, 12960, 16801, 24010, 30017, 40960, 49825, 65610, 78121, 100000, 117041, 146410, 168961, 207360, 236497, 285610, 322505, 384160, 430081, 506250, 562561, 655360, 723521, 835210 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A211064(n)+A211065(n)=n^4.

For a guide to related sequences, see A210000.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

FORMULA

From Chai Wah Wu, Nov 27 2016: (Start)

a(n) = n^4 - (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.: x*(-x^7 - 9*x^6 - 51*x^5 - 59*x^4 - 83*x^3 - 27*x^2 - 9*x - 1)/((x - 1)^5*(x + 1)^4). (End)

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]

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 *)

CROSSREFS

Cf. A210000.

Sequence in context: A102784 A294604 A061003 * A048879 A221805 A089211

Adjacent sequences:  A211061 A211062 A211063 * A211065 A211066 A211067

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 31 2012

STATUS

approved

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Last modified July 14 09:22 EDT 2020. Contains 335720 sequences. (Running on oeis4.)