A197652 Numbers that are congruent to 0 or 1 mod 10.

0, 1, 10, 11, 20, 21, 30, 31, 40, 41, 50, 51, 60, 61, 70, 71, 80, 81, 90, 91, 100, 101, 110, 111, 120, 121, 130, 131, 140, 141, 150, 151, 160, 161, 170, 171, 180, 181, 190, 191, 200, 201, 210, 211, 220, 221, 230, 231, 240, 241, 250, 251, 260, 261, 270, 271

Offset: 1

Author

Philippe Deléham, Oct 16 2011

Keywords

• nonn
• easy

Comments

From Wesley Ivan Hurt, Sep 26 2015: (Start)

Numbers with last digit 0 or 1.

Complement of (A260181 Union A262389). (End)

Numbers k such that floor(k/2) = 5*floor(k/10). - Bruno Berselli, Oct 05 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A020714, A030308, A260181, A262389.

Programs

Magma

[5*n-7-2*(-1)^n: n in [1..60]]; // Vincenzo Librandi, Jul 11 2012

Maple

A197652:=n->5*n-7-2*(-1)^n: seq(A197652(n), n=1..100); # Wesley Ivan Hurt, Sep 26 2015

Mathematica

CoefficientList[Series[x*(1+9*x)/((1+x)*(1-x)^2),{x,0,50}],x] (* Vincenzo Librandi, Jul 11 2012 *)

PARI

a(n)=n\2*10+n%2*9-9 \\ Charles R Greathouse IV, Oct 25 2011

Python

def A197652(n): return 5*n-(5 if n&1 else 9) # Chai Wah Wu, Oct 29 2024

Formula

a(n) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1 and b(k) = 5*2^k = A020714(k) for k>0.

From Zak Seidov, Oct 20 2011: (Start)

a(n) = a(n-2) + 10.

a(n) = 5*n - 7 - 2*(-1)^n. (End)

From Vincenzo Librandi, Jul 11 2012: (Start)

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

a(n) = a(n-1) + a(n-2) - a(n-3) for n>3. (End)

E.g.f.: 9 + (5*x - 7)*exp(x) - 2*exp(-x). - David Lovler, Sep 03 2022