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A144433
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Multiples of 8 interleaved with the sequence of odd numbers >= 3.
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8
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8, 3, 16, 5, 24, 7, 32, 9, 40, 11, 48, 13, 56, 15, 64, 17, 72, 19, 80, 21, 88, 23, 96, 25, 104, 27, 112, 29, 120, 31, 128, 33, 136, 35, 144, 37, 152, 39, 160, 41, 168, 43, 176, 45, 184, 47, 192, 49, 200, 51, 208, 53, 216, 55, 224, 57, 232, 59, 240, 61, 248, 63, 256, 65, 264
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OFFSET
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1,1
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COMMENTS
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For n >= 2, these are the numerators of 1/n^2 - 1/(n+1)^2: A061037(4), A061039(5), A061041(6), A061043(7), A061045(8), A061047(9), A061049(10), etc.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
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FORMULA
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a(2*n+1) = A008590(n+1), a(2*n) = A005408(n).
a(2*n+1) + a(2*n+2) = A017281(n+1).
From R. J. Mathar, Apr 01 2009: (Start)
a(n) = 2*a(n-2) - a(n-4).
G.f.: x*(8+3*x-x^3)/((1-x)^2*(1+x)^2). (End)
a(n) = 5+3/2*(-1)^(n-1)*(n-1)+3*(-1)^(n-1)+5/2*(n-1). - Paolo P. Lava, Apr 06 2009
a(n) = (n + 1) * 4^(n mod 2). - Wesley Ivan Hurt, Nov 27 2013
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MAPLE
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A144433:=n->(n+1)*4^(n mod 2); seq(A144433(n), n=1..100); # Wesley Ivan Hurt, Nov 27 2013
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MATHEMATICA
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Table[(n + 1)* 4^Mod[n, 2], {n, 100}] (* Wesley Ivan Hurt, Nov 27 2013 *)
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PROG
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(MAGMA) [5+3/2*(-1)^(n-1)*(n-1)+3*(-1)^(n-1)+5/2*(n-1): n in [1..70]]; // Vincenzo Librandi, Jul 30 2011
(PARI) x='x+O('x^50); Vec( x*(8+3*x-x^3)/((1-x)^2*(1+x)^2)) \\ G. C. Greubel, Sep 19 2018
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CROSSREFS
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Cf. A120070.
Sequence in context: A070608 A070486 A195161 * A274401 A228691 A228313
Adjacent sequences: A144430 A144431 A144432 * A144434 A144435 A144436
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Oct 04 2008
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EXTENSIONS
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Edited by R. J. Mathar, Apr 01 2009
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STATUS
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approved
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