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A211154 Number of 2 X 2 matrices having all terms in {-n,...,0,..,n} and even determinant. 3
41, 457, 1345, 4481, 8521, 18985, 30017, 54721, 78121, 126281, 168961, 252097, 322505, 454441, 562561, 759425, 916777, 1197001, 1416641, 1800961, 2097481, 2608937, 2998465, 3662401, 4162601, 5006665, 5636737, 6690881, 7471561, 8768041, 9721601, 11294977, 12445225, 14332361, 15704641 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

For a guide to related sequences, see A210000.

LINKS

Table of n, a(n) for n=1..35.

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*(-x^8 - 36*x^6 - 416*x^5 - 734*x^4 - 1472*x^3 - 724*x^2 - 416*x - 41)/((x - 1)^5*(x + 1)^4). (End)

MAPLE

seq((2*n+1)^4 - 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)^4 - 2*n*(1+n)*(1+3*n+3*n^2-(1+2*n)*(-1)^n); \\ Joerg Arndt, May 14 2013

CROSSREFS

Cf. A210000, A211155.

Sequence in context: A173768 A061643 A209842 * A103735 A177491 A269087

Adjacent sequences:  A211151 A211152 A211153 * A211155 A211156 A211157

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 05 2012

EXTENSIONS

More terms from Joerg Arndt, May 14 2013

STATUS

approved

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Last modified February 24 05:22 EST 2017. Contains 282560 sequences.