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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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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,2,0,-1).
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FORMULA
| 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 [From Paolo P. Lava (paoloplava(AT)gmail.com), Dec 12 2008]
a(n)a(n+1)=floor((n+2)/2). = A008619(n). [Paul Barry (pbarry(AT)wit.ie), Feb 27 2009
a(n)=sum{k=0..floor(n/2), C(n-k,k)*0^floor((n-2k)/2)}. [Paul Barry (pbarry(AT)wit.ie), Feb 27 2009
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PROG
| (PARI) Vec((1+x-x^2)/(1-2*x^2+x^4)+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012
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CROSSREFS
| Cf. A057979.
Sequence in context: A177815 A007879 A057979 * A133622 A158416 A162520
Adjacent sequences: A152268 A152269 A152270 * A152272 A152273 A152274
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KEYWORD
| nonn,easy
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 01 2008
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