A030110 a(n) = 2^n - n^2 + 1.

2, 2, 1, 0, 1, 8, 29, 80, 193, 432, 925, 1928, 3953, 8024, 16189, 32544, 65281, 130784, 261821, 523928, 1048177, 2096712, 4193821, 8388080, 16776641, 33553808, 67108189, 134217000, 268434673, 536870072, 1073740925, 2147482688

Offset: 0

Author

Steve Gray (stevebg(AT)roadrunner.com)

Keywords

• nonn
• easy

Links

• Matthew House, Table of n, a(n) for n = 0..3305
• Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Programs

Maple

A030110:=n->2^n-n^2+1: seq(A030110(n), n=0..50); # Wesley Ivan Hurt, Jan 15 2017

Mathematica

f[n_]:=2^n-n^2+1;f[Range[0,100]] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

Formula

G.f.: (2-8*x+9*x^2-x^3)/((1-2*x)*(1-x)^3).

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4). - Matthew House, Jan 15 2017