A176778 a(n) = 2^n - n*(n+2).

1, -1, -4, -7, -8, -3, 16, 65, 176, 413, 904, 1905, 3928, 7997, 16160, 32513, 65248, 130749, 261784, 523889, 1048136, 2096669, 4193776, 8388033, 16776592, 33553757, 67108136, 134216945, 268434616, 536870013, 1073740864, 2147482625, 4294966208, 8589933437, 17179867960

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Formula

G.f.: -(3*x-1)*(x^2-3*x+1)/((2*x-1)*(x-1)^3). - R. J. Mathar, Feb 18 2016

From Elmo R. Oliveira, Apr 03 2025: (Start)

E.g.f.: exp(x)*(exp(x) - x*(3 + x)).

a(n) = A000079(n) - A005563(n).

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4). (End)

Mathematica

Table[2^n-n*(n+2), {n, 0, 5!}]
LinearRecurrence[{5, -9, 7, -2}, {1, -1, -4, -7}, 40] (* Harvey P. Dale, Mar 14 2025 *)

Crossrefs

Cf. A000079, A005563, A014846, A142974, A176776, A176777.

Sequence in context: A190260 A318383 A151958 * A021213 A154687 A115021

Adjacent sequences: A176775 A176776 A176777 * A176779 A176780 A176781

Keyword

sign,easy

Author

Vladimir Joseph Stephan Orlovsky, Apr 25 2010

Status

approved