A176900 a(n) = sin((2*n+5)*Pi/6)*(n+1)*2^(n+1).

1, -4, -24, -32, 80, 384, 448, -1024, -4608, -5120, 11264, 49152, 53248, -114688, -491520, -524288, 1114112, 4718592, 4980736, -10485760, -44040192, -46137344, 96468992, 402653184, 419430400, -872415232, -3623878656, -3758096384

Offset: 0

Author

Jaume Oliver Lafont, Apr 28 2010

Keywords

• sign

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-12,16,-16).

Crossrefs

Cf. A002162.

Programs

Mathematica

Table[Sin[(2*n + 5)*Pi/6]*(n + 1)*2^(n + 1), {n, 0, 27}] (* Amiram Eldar, Feb 26 2022 *)

PARI

a(n)=[1,-1,-2,-1,1,2][n%6+1]*(n+1)*2^n

Formula

Sum_{k>=0} 1/a(k) = log(2), from log((1+x)/(1-x+x^2)) at x=1/2.

G.f.: (1-8*x+4*x^2)/(1-2*x+4*x^2)^2.

Sum_{n>=0} (-1)^n/a(n) = log(7/2). - Amiram Eldar, Feb 26 2022