A216714 a(n) = 2^(n-5) - A000931(n).

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

Offset: 5

Author

N. J. A. Sloane, Sep 14 2012

Keywords

• nonn
• easy

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)

Crossrefs

Cf. A000931, A038360.

Programs

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

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 *)
LinearRecurrence[{2,1,-1,-2},{0,1,3,6},40] (* Harvey P. Dale, Aug 22 2021 *)

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

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