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A216714
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a(n) = 2^(n-5) - A000931(n).
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2
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0, 1, 3, 6, 14, 29, 60, 123, 249, 503, 1012, 2032, 4075, 8164, 16347, 32719, 65471, 130986, 262030, 524137, 1048376, 2096887, 4193953, 8388143, 16776600, 33553616, 67107783, 134216296, 268433559, 536868399, 1073738495, 2147479238, 4294961454, 8589926853, 17179858932, 34359724787, 68719458745, 137438929639, 274877875372, 549755772064
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OFFSET
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5,3
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COMMENTS
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It is conjectured that this sequence (with a different offset) and A038360 are the same.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 5..1000
P. Flajolet and B. Salvy, Euler sums and contour integral representations, Experimental Mathematics, Vol. 7 Issue 1 (1998).
M. Waldschmidt, Lectures on Multiple Zeta Values (IMSC2011).
Index entries for linear recurrences with constant coefficients, signature (2,1,-1,-2)
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FORMULA
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G.f.: -x^6*(-1-x+x^2) / ( (2*x-1)*(x^3+x^2-1) ). - R. J. Mathar, Sep 16 2012
a(n) = 2*a(n-1)+a(n-2)-a(n-3)-2*a(n-4). - Vincenzo Librandi, Mar 11 2013
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MATHEMATICA
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CoefficientList[Series[-x (-1 - x + x^2)/((2 x - 1) (x^3 + x^2 - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 11 2013 *)
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PROG
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(MAGMA) I:=[0, 1, 3, 6]; [n le 4 select I[n] else 2*Self(n-1)+Self(n-2)-Self(n-3)-2*Self(n-4): n in [1..40]]; // Vincenzo Librandi, Mar 11 2013
(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -2, -1, 1, 2]^(n-5)*[0; 1; 3; 6])[1, 1] \\ Charles R Greathouse IV, Sep 09 2016
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CROSSREFS
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Cf. A000931, A038360.
Sequence in context: A219768 A038359 A038360 * A084174 A036658 A307457
Adjacent sequences: A216711 A216712 A216713 * A216715 A216716 A216717
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Sep 14 2012
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STATUS
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approved
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