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 A097065 Interleave n+1 and n-1. 7
 1, -1, 2, 0, 3, 1, 4, 2, 5, 3, 6, 4, 7, 5, 8, 6, 9, 7, 10, 8, 11, 9, 12, 10, 13, 11, 14, 12, 15, 13, 16, 14, 17, 15, 18, 16, 19, 17, 20, 18, 21, 19, 22, 20, 23, 21, 24, 22, 25, 23, 26, 24, 27, 25, 28, 26, 29, 27, 30, 28, 31, 29, 32, 30, 33, 31, 34, 32, 35, 33, 36, 34, 37, 35, 38 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Pairwise sums are abs(A023443), or n-1+2*0^n. The partial sums of this sequence is A000124, with extra leading 1. Partial sums are A097066. Binomial transform is A097067. LINKS Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA G.f.: (1-2x+2x^2)/((1+x)(1-x)^2). a(n) = (2n-1)/4 + 5(-1)^n/4. a(n) = floor((n+2)/2) - 2 * (n mod 2). - Reinhard Zumkeller, Apr 06 2015 a(n) = a(n-1) + a(n-2) - a(n-3) for n > 2. - Wesley Ivan Hurt, Jan 10 2017 MAPLE A097065:=n->(2*n-1)/4 + 5*(-1)^n/4: seq(A097065(n), n=0..150); # Wesley Ivan Hurt, Jan 10 2017 MATHEMATICA Table[(2n - 1)/4 + 5(-1)^n/4, {n, 0, 75}] (* Or *) Flatten[ Table[{n + 1, n - 1}, {n, 0, 37}]] (* Or *) CoefficientList[Series[(1 - 2x + 2x^2)/((1 + x)(1 - x)^2), {x, 0, 75}], x] (* Robert G. Wilson v, Jul 24 2004 *) PROG (Haskell) import Data.List (transpose) a097065 n = n' - 2 * m where (n', m) = divMod (n + 2) 2 a097065_list = concat \$ transpose [[1 ..], [-1 ..]] (PARI) a(n)=n\2+1-n%2*2 \\ Charles R Greathouse IV, Sep 02 2015 (MAGMA) [(2*n-1)/4 + 5*(-1)^n/4 : n in [0..100]]; // Wesley Ivan Hurt, Jan 10 2017 CROSSREFS Essentially the same as A084964. Cf. A000124, A023443, A097066, A097067. Sequence in context: A025636 A025637 A195826 * A084964 A267182 A008720 Adjacent sequences:  A097062 A097063 A097064 * A097066 A097067 A097068 KEYWORD easy,sign AUTHOR Paul Barry, Jul 22 2004 STATUS approved

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Last modified September 18 22:16 EDT 2019. Contains 327183 sequences. (Running on oeis4.)