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A152271
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a(n)=1 for even n and (n+1)/2 for odd n.
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14
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1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 11, 1, 12, 1, 13, 1, 14, 1, 15, 1, 16, 1, 17, 1, 18, 1, 19, 1, 20, 1, 21, 1, 22, 1, 23, 1, 24, 1, 25, 1, 26, 1, 27, 1, 28, 1, 29, 1, 30, 1, 31, 1, 32, 1, 33, 1, 34, 1, 35, 1, 36, 1, 37, 1, 38, 1, 39, 1, 40, 1, 41, 1, 42, 1, 43, 1, 44
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OFFSET
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0,4
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COMMENTS
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A000012 and A000027 interleaved. - Omar E. Pol, Mar 12 2012
Run lengths in A128218. - Reinhard Zumkeller, Jun 20 2015
a(n+1) is the number of reversible binary strings of length n+1 with Hamming weight 1 or 2 such that the 1's are separated by an even number of 0's. - Christian Barrientos, Jan 28 2019
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LINKS
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Table of n, a(n) for n=0..87.
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
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FORMULA
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a(n) = 2*a(n-2) - a(n-4) with a(0)=a(1)=a(2)=1 and a(3)=2.
a(n) = (a(n-2) + a(n-3))/a(n-1).
G.f.: (1 + x - x^2)/(1 - 2*x^2 + x^4).
a(n) = A057979(n+2).
a(n) = (1/4)*(3 + n + (1-n)*(-1)^n), with n >= 0. - Paolo P. Lava, Dec 12 2008
a(n)*a(n+1) = floor((n+2)/2) = A008619(n). - Paul Barry, Feb 27 2009
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)*0^floor((n-2k)/2). - Paul Barry, Feb 27 2009
a(n) = gcd(floor((n+1)/2), (n+1)). - Enrique Pérez Herrero, Mar 13 2012
G.f.: U(0) where U(k) = 1 + x*(k+1)/(1 - x/(x + (k+1)/U(k+1))) ; (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 04 2012
E.g.f.: ((2 + x)*cosh(x) + sinh(x))/2. - Stefano Spezia, Mar 26 2022
a(n) = (-1)^n * a(-2-n) for all n in Z. - Michael Somos, Mar 26 2022
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EXAMPLE
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G.f. = 1 + x + x^2 + 2*x^3 + x^4 + 3*x^5 + x^6 + 4*x^7 + x^8 + ... - Michael Somos, Mar 26 2022
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MATHEMATICA
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Table[If[EvenQ[n], 1, (n+1)/2], {n, 0, 120}] (* or *) LinearRecurrence[{0, 2, 0, -1}, {1, 1, 1, 2}, 120] (* or *) Riffle[Range[60], 1, {1, -1, 2}] (* Harvey P. Dale, Jan 20 2018 *)
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PROG
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(PARI) Vec((1+x-x^2)/(1-2*x^2+x^4)+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012
(PARI) a(n)=gcd(n+1, (n+1)\2) \\ Charles R Greathouse IV, Mar 13 2012
(Haskell)
import Data.List (transpose)
a152271 = a057979 . (+ 2)
a152271_list = concat $ transpose [repeat 1, [1..]]
-- Reinhard Zumkeller, Aug 11 2014
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CROSSREFS
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Cf. A000012, A000027, A008619, A057979, A128218.
Sequence in context: A177815 A007879 A057979 * A133622 A158416 A318225
Adjacent sequences: A152268 A152269 A152270 * A152272 A152273 A152274
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KEYWORD
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nonn,easy
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AUTHOR
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Philippe Deléham, Dec 01 2008
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STATUS
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approved
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