Revision History for A211157
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
|
|
|
|
#6 by Jon E. Schoenfield at Tue Jan 10 22:06:47 EST 2017
|
|
|
|
#5 by Jon E. Schoenfield at Tue Jan 10 22:06:45 EST 2017
|
| NAME
|
Number of 2 X 2x22 matrices having all terms in {-n,...,0,..,n} and positive even determinant.
|
| STATUS
|
approved
editing
|
|
|
|
#4 by T. D. Noe at Tue Apr 10 18:57:54 EDT 2012
|
|
|
|
#3 by Clark Kimberling at Tue Apr 10 18:07:53 EDT 2012
|
|
|
|
#2 by Clark Kimberling at Thu Apr 05 17:04:12 EDT 2012
|
| NAME
|
allocatedNumber of 2x2 matrices having all terms in {-n,...,0,..,n} and forpositive Clarkeven Kimberlingdeterminant.
|
| DATA
|
4, 164, 528, 1968, 3844, 8836, 14144, 26176, 37540, 61188, 82192, 123120, 157924, 223268, 276608, 374272, 452420, 591524, 700752, 891760, 1038980, 1293700, 1487744, 1818112, 2067172
|
| OFFSET
|
1,1
|
| COMMENTS
|
For a guide to related sequences, see A210000.
|
| 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 *)
|
| CROSSREFS
|
Cf. A210000.
|
| KEYWORD
|
allocated
nonn
|
| AUTHOR
|
Clark Kimberling, Apr 05 2012
|
| STATUS
|
approved
editing
|
|
|
|
#1 by Clark Kimberling at Mon Apr 02 21:39:37 EDT 2012
|
| NAME
|
allocated for Clark Kimberling
|
| KEYWORD
|
allocated
|
| STATUS
|
approved
|
|
|
|
|