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A211158 Number of 2 X 2 matrices having all terms in {-n,...,0,..,n} and positive odd determinant. 4
20, 84, 528, 1040, 3060, 4788, 10304, 14400, 26100, 34100, 55440, 69264, 104468, 126420, 180480, 213248, 291924, 338580, 448400, 512400, 660660, 745844, 940608, 1051200, 1301300, 1441908, 1756944, 1932560, 2322900, 2538900, 3015680, 3277824, 3852948, 4167380 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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, Dec 13 2016: (Start)

For n >= 0:

a(n) = A211155(n)/2.

a(n) = n*(n + 1)*(3*n + 1 + 3*n^2 - (-1)^n*(2*n + 1)). Therefore:

a(n) = n^2*(n + 1)*(3*n + 1) if n is even,

a(n) = n*(n + 1)^2*(3*n + 2) if n is odd.

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*(-20*x^6 - 64*x^5 - 364*x^4 - 256*x^3 - 364*x^2 - 64*x - 20)/((x - 1)^5*(x + 1)^4). (End)

a(n) = a(-n-1). - Bruno Berselli, Dec 14 2016

MATHEMATICA

a = -n; b = n; z1 = 25;

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_] := u[n] = Sum[c[n, 2 k], {k, 0, 2*n^2}]

v[n_] := v[n] = Sum[c[n, 2 k], {k, 1, 2*n^2}]

w[n_] := w[n] = Sum[c[n, 2 k - 1], {k, 1, 2*n^2}]

u1 = Table[u[n], {n, 1, z1}] (* A211156 *)

v1 = Table[v[n], {n, 1, z1}] (* A211157 *)

w1 = Table[w[n], {n, 1, z1}] (* A211158 *)

(u1 - 1)/4 (* integers *)

v1/4 (* integers *)

w1/4 (* integers *)

Table[n*(n+1)*(3*n+1+3*n^2-(-1)^n*(2*n+1)), {n, 35}] (* Vincenzo Librandi, Dec 14 2016 *)

CoefficientList[ Series[-(( 4(5 + 16x + 91x^2 + 64x^3 + 91x^4 + 16x^5 + 5x^6))/((x -1)^5 (x +1)^4)), {x, 0, 35}], x] (* or *)

LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {20, 84, 528, 1040, 3060, 4788, 10304, 14400, 26100}, 36] (* Robert G. Wilson v, Dec 14 2016 *)

PROG

(Python)

def A211158(n):

    return n*(n+1)*(3*n+1+3*n**2-(-1)**n*(2*n+1)) # Chai Wah Wu, Dec 13 2016

(MAGMA) [n*(n+1)*(3*n+1+3*n^2-(-1)^n*(2*n+1)): n in [1..35]]; // Vincenzo Librandi, Dec 14 2016

CROSSREFS

Cf. A210000.

Sequence in context: A006566 A205312 A268888 * A154077 A027849 A243645

Adjacent sequences:  A211155 A211156 A211157 * A211159 A211160 A211161

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 05 2012

STATUS

approved

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Last modified September 27 10:28 EDT 2021. Contains 347689 sequences. (Running on oeis4.)