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A097140
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Interleave n and 1-n.
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3
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0, 1, 1, 0, 2, -1, 3, -2, 4, -3, 5, -4, 6, -5, 7, -6, 8, -7, 9, -8, 10, -9, 11, -10, 12, -11, 13, -12, 14, -13, 15, -14, 16, -15, 17, -16, 18, -17, 19, -18, 20, -19, 21, -20, 22, -21, 23, -22, 24, -23, 25, -24, 26, -25, 27, -26, 28, -27, 29, -28, 30, -29, 31, -30, 32, -31
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OFFSET
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0,5
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COMMENTS
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Partial sums are A097141. Binomial transform is x(1+x)/(1-2x), or A003945 with a leading 0.
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LINKS
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FORMULA
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G.f.: x*(1 + 2*x)/((1 - x)*(1 + x)^2).
a(n) = 3/4 + (2*n - 3)*(-1)^n/4.
a(0)=0, a(1)=1, a(2)=1, a(n)=a(n-1)+a(n-2)+a(n-3). - Harvey P. Dale, Mar 26 2012
G.f.: x*G(0)/(1+x) where G(k) = 1 + 2*x/(1 - x/(x + 2/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Dec 21 2012
E.g.f.: ((3 + x)*sinh(x) - x*cosh(x))/2. - Stefano Spezia, Mar 07 2023
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MATHEMATICA
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With[{nn=35}, Riffle[Range[0, nn], Range[1, -(nn-1), -1]]] (* or *) LinearRecurrence[ {-1, 1, 1}, {0, 1, 1}, 70] (* Harvey P. Dale, Mar 26 2012 *)
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PROG
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(Haskell)
import Data.List (transpose)
a097140 n = a097140_list !! n
a097140_list = concat $ transpose [a001477_list, map (1 -) a001477_list]
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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