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A280747
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One of a set of five sequences arising in the enumeration of optimal {0,1,-1}-configurations.
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5
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1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 4, 3, 3, 2, 2, 2, 4, 2, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 2, 2, 1, 1, 2, 1, 3, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 4, 4, 4, 2
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OFFSET
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0,4
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LINKS
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FORMULA
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See Maple code for the five recurrences.
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MAPLE
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for p from 1 to 5 do u[p][0]:=1; od;
u[1][1]:=1; u[2][1]:=1; u[3][1]:=0; u[4][1]:=0; u[5][1]:=0;
for n from 2 to 100 do
if n mod 2 = 0 then
u[1][n]:=u[1][n/2]; u[2][n]:=u[1][n/2]; u[3][n]:=u[2][n/2]; u[4][n]:=u[1][n/2]; u[5][n]:=u[4][n/2];
else
u[1][n]:=u[2][(n-1)/2]+u[4][(n+1)/2]; u[2][n]:=u[3][(n-1)/2]; u[3][n]:=0; u[4][n]:=u[5][(n-1)/2]; u[5][n]:=0;
fi;
od:
[seq(u[1][n], n=0..100)]; # A280747
[seq(u[2][n], n=0..100)]; # A280748
[seq(u[3][n], n=0..100)]; # A280749
[seq(u[4][n], n=0..100)]; # A280750
[seq(u[5][n], n=0..100)]; # A280751
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MATHEMATICA
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For[p = 1, p <= 5, p++, u[p][0] = 1]; u[1][1] = 1; u[2][1] = 1; u[3][1] = 0; u[4][1] = 0; u[5][1] = 0;
For[n = 2, n <= 100, n++, If[Mod[n, 2] == 0, u[1][n] = u[1][n/2]; u[2][n] = u[1][n/2]; u[3][n] = u[2][n/2]; u[4][n] = u[1][n/2]; u[5][n] = u[4][n/2], u[1][n] = u[2][(n-1)/2] + u[4][(n+1)/2]; u[2][n] = u[3][(n-1)/2]; u[3][n] = 0; u[4][n] = u[5][(n-1)/2]; u[5][n] = 0]];
Table[u[1][n], {n, 0, 100}] (* A280747 *)
Table[u[2][n], {n, 0, 100}] (* A280748 *)
Table[u[3][n], {n, 0, 100}] (* A280749 *)
Table[u[4][n], {n, 0, 100}] (* A280750 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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