A029929 a(n) = n*(n + ceiling(2^n/12)).

0, 2, 6, 12, 24, 40, 72, 126, 240, 468, 960, 2002, 4248, 9048, 19320, 41190, 87648, 185980, 393552, 830490, 1748040, 3670464, 7690056, 16078702, 33555024, 69905700, 145403232, 301990626, 626350200, 1297438888, 2684355480, 5547667062, 11453247168, 23622321228, 48676297200, 100215904810

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

C. Musès, The dimensional family approach in (hyper)sphere packing..., Applied Math. Computation 88 (1997), pp. 1-26, see p. 7.

Index entries for linear recurrences with constant coefficients, signature (5,-6,-6,15,-3,-8,4).

Formula

a(n) = n*(6+2*(-1)^n+2^n+12*n)/12. G.f.: 2*x*(x^7 -2*x^6 -2*x^5 +x^4 -6*x^3 +3*x^2 +2*x -1) / ((x-1)^3*(x+1)^2*(2*x-1)^2). - Colin Barker, Aug 04 2013

Mathematica

CoefficientList[Series[2 x (x^7 - 2 x^6 - 2 x^5 + x^4 - 6 x^3 + 3 x^2 + 2 x - 1)/((x - 1)^3 (x + 1)^2 (2 x - 1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 19 2013 *)
Table[n(n+Ceiling[2^n/12]), {n, 0, 40}] (* or *) LinearRecurrence[{5, -6, -6, 15, -3, -8, 4}, {0, 2, 6, 12, 24, 40, 72, 126, 240}, 50] (* Harvey P. Dale, Sep 05 2020 *)

Prog

(PARI) a(n)  = n*(n + ceil(2^n/12)) \\ Michel Marcus, May 11 2013
(Magma) [n*(n + Ceiling(2^n/12)): n in [0..40]]; // Vincenzo Librandi, Oct 19 2013

Crossrefs

Sequence in context: A001116 A002336 A030625 * A222785 A053635 A054061

Adjacent sequences: A029926 A029927 A029928 * A029930 A029931 A029932

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Added more terms, Joerg Arndt, May 11 2013

Status

approved