

A211154


Number of 2x2 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
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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.


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: A061643 A037061 A209842 * A103735 A177491 A166843
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



