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A211155 Number of 2 X 2 matrices having all terms in {-n,...,0,..,n} and odd determinant. 4
0, 40, 168, 1056, 2080, 6120, 9576, 20608, 28800, 52200, 68200, 110880, 138528, 208936, 252840, 360960, 426496, 583848, 677160, 896800, 1024800, 1321320, 1491688, 1881216, 2102400, 2602600, 2883816, 3513888, 3865120, 4645800, 5077800, 6031360, 6555648, 7705896, 8334760, 9707040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A211154(n) + A211155(n) = (2n+1)^4.

For a guide to related sequences, see A210000.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1000

FORMULA

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

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*(-40*x^6 - 128*x^5 - 728*x^4 - 512*x^3 - 728*x^2 - 128*x - 40)/((x - 1)^5*(x + 1)^4). (End)

MAPLE

seq( 2*n*(1+n)*(1+3*n+3*n^2-(1+2*n)*(-1)^n), n=1..20); # Mark van Hoeij, May 13 2013

MATHEMATICA

a = -n; b = n; z1 = 20;

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}] (* A211154 *)

Table[v[n], {n, 1, z1}] (* A211155 *)

PROG

(PARI) a(n)=2*n*(1+n)*(1+3*n+3*n^2-(1+2*n)*(-1)^n); \\ Joerg Arndt, May 14 2013

CROSSREFS

Cf. A210000.

Sequence in context: A250585 A260169 A205249 * A250994 A250995 A262487

Adjacent sequences:  A211152 A211153 A211154 * A211156 A211157 A211158

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 05 2012

EXTENSIONS

More terms from Joerg Arndt, May 14 2013

a(0)=0 prepended by Andrew Howroyd, May 05 2020

STATUS

approved

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Last modified September 18 04:22 EDT 2021. Contains 347508 sequences. (Running on oeis4.)