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A210379 Number of 2 X 2 matrices with all terms in {0,1,...,n} and odd trace. 4
0, 8, 36, 128, 300, 648, 1176, 2048, 3240, 5000, 7260, 10368, 14196, 19208, 25200, 32768, 41616, 52488, 64980, 80000, 97020, 117128, 139656, 165888, 195000, 228488, 265356, 307328, 353220, 405000, 461280, 524288, 592416, 668168 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A210379(n)+A210378(n)=(n+1)^4.

See A210000 for a guide to related sequences.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..10000

FORMULA

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

a(n) = (n + 1)^2*((n + 1)^2 - (2*n + 1 -(-1)^n)^2/16 - (2*n + 3 + (-1)^n)^2/16).

a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) for n > 7.

G.f.: -4*x*(2*x^4 + 5*x^3 + 10*x^2 + 5*x + 2)/((x - 1)^5*(x + 1)^3). (End)

EXAMPLE

Writing the matrices as 4-letter words, the 8 for n=1 are as follows:

1000, 1100, 1010, 1110, 0001, 0011, 0101, 0111

MATHEMATICA

a = 0; b = n; z1 = 35;

t[n_] := t[n] = Flatten[Table[w + z, {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, 0, 2*n}]

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

Table[u[n], {n, 0, z1}] (* A210378 *)

Table[v[n], {n, 0, z1}] (* A210379 *)

CROSSREFS

Cf. A210000, A210378.

Sequence in context: A054470 A213581 A276279 * A131123 A055910 A022573

Adjacent sequences:  A210376 A210377 A210378 * A210380 A210381 A210382

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 20 2012

STATUS

approved

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Last modified August 19 01:35 EDT 2017. Contains 290788 sequences.