A373565 Expansion of x + 1/(1 - x).

1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,2

Links

Table of n, a(n) for n=0..84.

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

a(n) = [x^n] (x^2 - x - 1) / (x - 1).

E.g.f.: exp(x) + x. - Stefano Spezia, Jun 10 2024

Mathematica

Table[Piecewise[{{2, n == 1}}, 1], {n, 0, 20}] (* Eric W. Weisstein, Dec 28 2025 *)
Table[If[n == 1, 2, 1], {n, 0, 20}] (* Eric W. Weisstein, Dec 28 2025 *)
1 + Table[Boole[n == 1], {n, 0, 20}] (* Eric W. Weisstein, Dec 28 2025 *)

Crossrefs

Cf. A294619 (a(0) = 0, a(1) = 1, a(2) = 2 and a(n) = 1 for n > 2).

Sequence in context: A369162 A329684 A294619 * A054977 A272901 A078315

Adjacent sequences: A373562 A373563 A373564 * A373566 A373567 A373568

Keyword

nonn,easy

Author

Peter Luschny, Jun 10 2024

Status

approved