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A193777
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Number of signed permutations of size 2n invariant under D and D'bar and avoiding (-2, 1) and (2, -1).
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3
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1, 2, 6, 18, 58, 190, 642, 2206, 7746, 27662, 100738, 373550, 1413506, 5457710, 21546466, 87025806, 360264258, 1529624366, 6669850466, 29877013902, 137560725890, 650780790894, 3162711095074, 15774862353614, 80687636530882, 422713072650286, 2265833731786594
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OFFSET
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0,2
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COMMENTS
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Also the number of signed permutations of size n invariant under D and avoiding (-2, 1) and (2, -1).
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LINKS
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FORMULA
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a(n) = 2*a(n-1) + n*a(n-2) - Sum_{j=1..k-3} j*a(j)*|S_{k-j-3}^D|, where S_n^D is the set of unsigned permutations of length n invariant under D.
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MAPLE
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inv := proc(n) option remember; if n<2 then 1 else inv(n-1)+(n-1)*inv(n-2) fi end:
a := proc(n) option remember; if n < 2 then n+1 else
2*a(n-1) + n*a(n-2) - add(j*a(j)*inv(n-j-2), j=1..n-3) fi end:
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MATHEMATICA
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inv[n_] := inv[n] = If[n<2, 1, inv[n-1] + (n-1) inv[n-2]];
a[n_] := a[n] = If[n<2, n+1, 2 a[n-1] + n a[n-2] - Sum[j a[j] inv[n-j-2], {j, 1, n-3}]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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