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A211154
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Number of 2x2 matrices having all terms in {-n,...,0,..,n} and even determinant.
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3
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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
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1,1
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COMMENTS
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A211154(n)+A211155(n)=(2n+1)^4.
For a guide to related sequences, see A210000.
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LINKS
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Table of n, a(n) for n=1..35.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A210000, A211155.
Sequence in context: A061643 A037061 A209842 * A103735 A177491 A166843
Adjacent sequences: A211151 A211152 A211153 * A211155 A211156 A211157
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KEYWORD
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nonn,changed
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AUTHOR
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Clark Kimberling, Apr 05 2012
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EXTENSIONS
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More terms from Joerg Arndt, May 14 2013
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STATUS
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approved
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