A022958 a(n) = 2 - n.

2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, -50, -51, -52, -53, -54, -55

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

Comments

a(n) is the Euler characteristic of one-sided surface of genus n (see Courant and Herbert). - Stefano Spezia, Sep 10 2022

Links

• Richard Courant and Herbert Robbins, What Is Mathematics?, Oxford, 1941, p. 262.
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A239229.

Programs

Mathematica

2-Range[0,60] (* or *) LinearRecurrence[{2,-1},{2,1},60] (* Harvey P. Dale, Feb 23 2023 *)

PARI

a(n)=n-2 \\ Charles R Greathouse IV, Jun 11 2015

Formula

From Paul Barry, Mar 31 2007: (Start)

G.f.: (2-3x)/(1-x)^2.

E.g.f.: exp(x)*(2-x). (End)

a(n) = 2*a(n-1) - a(n-2); a(0)=2, a(1)=1. - Philippe Deléham, Nov 03 2008