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

1,3

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).

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

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 *)

Prog

(PARI) a(n)=n\2*10+n%2*9-9 \\ Charles R Greathouse IV, Oct 25 2011
(Magma) [5*n-7-2*(-1)^n: n in [1..60]]; // Vincenzo Librandi, Jul 11 2012
(Python)
def A197652(n): return 5*n-(5 if n&1 else 9) # Chai Wah Wu, Oct 29 2024

Crossrefs

Cf. A020714, A030308, A260181, A262389.

Sequence in context: A329818 A329447 A352339 * A261909 A325483 A235202

Adjacent sequences: A197649 A197650 A197651 * A197653 A197654 A197655

Keyword

nonn,easy

Author

Philippe Deléham, Oct 16 2011

Status

approved