Revision History for A211157
(Underlined text is an addition;
strikethrough text is a deletion.)
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#6 by Jon E. Schoenfield at Tue Jan 10 22:06:47 EST 2017
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#5 by Jon E. Schoenfield at Tue Jan 10 22:06:45 EST 2017
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| NAME
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Number of 2 X 2x22 matrices having all terms in {-n,...,0,..,n} and positive even determinant.
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| STATUS
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approved
editing
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#4 by T. D. Noe at Tue Apr 10 18:57:54 EDT 2012
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#3 by Clark Kimberling at Tue Apr 10 18:07:53 EDT 2012
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#2 by Clark Kimberling at Thu Apr 05 17:04:12 EDT 2012
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| NAME
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allocatedNumber of 2x2 matrices having all terms in {-n,...,0,..,n} and forpositive Clarkeven Kimberlingdeterminant.
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| DATA
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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
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| OFFSET
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1,1
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| COMMENTS
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For a guide to related sequences, see A210000.
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| MATHEMATICA
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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 *)
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| CROSSREFS
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Cf. A210000.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Clark Kimberling, Apr 05 2012
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| STATUS
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approved
editing
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#1 by Clark Kimberling at Mon Apr 02 21:39:37 EDT 2012
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| NAME
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allocated for Clark Kimberling
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| KEYWORD
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allocated
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| STATUS
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approved
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