A239229 Euler characteristic of n-holed torus: 2 - 2*n.

2, 0, -2, -4, -6, -8, -10, -12, -14, -16, -18, -20, -22, -24, -26, -28, -30, -32, -34, -36, -38, -40, -42, -44, -46, -48, -50, -52, -54, -56, -58, -60, -62, -64, -66, -68, -70, -72, -74, -76, -78, -80, -82, -84, -86, -88, -90, -92, -94, -96, -98, -100, -102

Offset: 0

Author

Eric M. Schmidt, Mar 12 2014

Keywords

• sign
• easy

References

• Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §12.4 Theorems and Formulas (Plane Geometry), p. 450.
• James Munkres, Topology, 2nd ed., Pearson, 2000.

Links

• Richard Courant and Herbert Robbins, What Is Mathematics?, Oxford, 1941, pp. 258-259.
• Eric Weisstein's World of Mathematics, Euler Characteristic.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A010673, A022958.

Programs

Magma

[2-2*n: n in [0..60]]; // Vincenzo Librandi, Feb 01 2015

Maple

A239229:=n->2 - 2*n; seq(A239229(n), n=0..100); # Wesley Ivan Hurt, Mar 15 2014

Mathematica

Table[2 - 2 n, {n, 0, 100}] (* Wesley Ivan Hurt, Mar 15 2014 *)
LinearRecurrence[{2,-1},{2,0},80] (* Harvey P. Dale, Jan 31 2015 *)
CoefficientList[Series[2 (1-2 x) / (1 - x)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Feb 01 2015 *)

Formula

a(n) = 2 - 2*n.

G.f.: 2*(1-2*x)/(1-x)^2. - Vincenzo Librandi, Feb 01 2015

a(n) = 2*A022958(n+1). - R. J. Mathar, Oct 05 2017

E.g.f.: 2*exp(x)*(1 - x). - Stefano Spezia, Sep 10 2022