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A216714 a(n) = 2^(n-5) - A000931(n). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,3

COMMENTS

It is conjectured that this sequence (with a different offset) and A038360 are the same.

LINKS

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)

FORMULA

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

MATHEMATICA

CoefficientList[Series[-x (-1 - x + x^2)/((2 x - 1) (x^3 + x^2 - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 11 2013 *)

PROG

(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

CROSSREFS

Cf. A000931, A038360.

Sequence in context: A219768 A038359 A038360 * A084174 A036658 A307457

Adjacent sequences:  A216711 A216712 A216713 * A216715 A216716 A216717

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 14 2012

STATUS

approved

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Last modified May 6 08:24 EDT 2021. Contains 343580 sequences. (Running on oeis4.)