A242709 Nonequivalent ways to place two different markers (e.g., a pair of Go stones, black and white) on an n X n grid.
0, 2, 12, 33, 85, 165, 315, 518, 846, 1260, 1870, 2607, 3627, 4823, 6405, 8220, 10540, 13158, 16416, 20045, 24465, 29337, 35167, 41538, 49050, 57200, 66690, 76923, 88711, 101355, 115785, 131192, 148632, 167178, 188020, 210105, 234765, 260813, 289731, 320190
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).
Crossrefs
Cf. A014409 (with indistinguishable checkers)
Programs
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Magma
[n*(n^3 + n*3^(n mod 2) - 2*2^(n mod 2))/8: n in [1..50]]; // Wesley Ivan Hurt, May 21 2014
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Maple
A242709:=n->n*(n^3 + n*3^(n mod 2) - 2*2^(n mod 2))/8; seq(A242709(n), n=1..50); # Wesley Ivan Hurt, May 21 2014
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Mathematica
f[n_] := If[OddQ[n], (n^3 + 3 n - 4), (n^3 + n - 2)] n/8; Table[f[n], {n, 1, 40}] -
PARI
concat(0, Vec(-x^2*(x^5+x^4+7*x^3+5*x^2+8*x+2)/((x-1)^5*(x+1)^3) + O(x^100))) \\ Colin Barker, May 21 2014
Formula
For odd n, a(n) = n*(n^3 + 3*n - 4)/8.
For even n, a(n) = n*(n^3 + n - 2)/8.
G.f.: -x^2*(x^5+x^4+7*x^3+5*x^2+8*x+2) / ((x-1)^5*(x+1)^3). - Colin Barker, May 21 2014
a(n) = n*(n^3 + n*3^(n mod 2) - 2*2^(n mod 2))/8. - Wesley Ivan Hurt, May 21 2014
Comments