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A320667
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First differences of A066194.
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0
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1, 2, -1, 5, -1, -2, 1, 10, -1, -2, 1, -5, 1, 2, -1, 21, -1, -2, 1, -5, 1, 2, -1, -10, 1, 2, -1, 5, -1, -2, 1, 42, -1, -2, 1, -5, 1, 2, -1, -10, 1, 2, -1, 5, -1, -2, 1, -21, 1, 2, -1, 5, -1, -2, 1, 10, -1, -2, 1, -5, 1, 2, -1, 85, -1, -2, 1, -5, 1, 2, -1, -10
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listen;
history;
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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To obtain the first 2^n-1 entries if you have the first 2^(n-1)-1 entries, adjoin 1/6 (-3 + (-1)^(1 + n) + 2^(2 + n)) to the right end of the list, negate the signs of the first 2^(n-1)-1 entries, and then adjoin that list to the right. For example for n=3 {1,2,-1} becomes {1,2,-1,5,-1,-2,1}.
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MATHEMATICA
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Fold[Join[#1, {#2}, -#1] &, {1},
Table[1/6 (-3 + (-1)^(1 + n) + 2^(2 + n)), {n, 2, 6}]]
t[n_/; IntegerQ[Log2[n]]]:=1/6 (-3 + (-1)^IntegerExponent[n, 2] + 8*n);
t[n_/; Not[IntegerQ[Log2[n]]]]:=-t[n-2^Floor[Log2[n]]];
Table[t[j], {j, 1, 15}](* recursive formulation *)
Table[1/6 (-3+(-1)^IntegerExponent[j, 2]+2^(IntegerExponent[j, 2]+3))(-1)^(Total[IntegerDigits[j, 2]]+1), {j, 1, 15}] (* closed form *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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