A047216 Numbers that are congruent to {1, 2} mod 5.

1, 2, 6, 7, 11, 12, 16, 17, 21, 22, 26, 27, 31, 32, 36, 37, 41, 42, 46, 47, 51, 52, 56, 57, 61, 62, 66, 67, 71, 72, 76, 77, 81, 82, 86, 87, 91, 92, 96, 97, 101, 102, 106, 107, 111, 112, 116, 117, 121, 122, 126, 127, 131, 132, 136, 137, 141, 142, 146, 147

Offset

1,2

Comments

Equivalently, numbers ending in 1, 2, 6 and 7. - Bruno Berselli, Sep 04 2018

Links

David Lovler, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 5*n-a(n-1)-7 for n>1, with a(1)=1. - Vincenzo Librandi, Aug 05 2010

G.f.: x*(1+x+3*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Bruno Berselli, Mar 10 2012: (Start)

a(n) = (10*n-3*(-1)^n-9)/4.

a(n) = - A176059(n) + Sum_{i=0..n-1} A176059(i). (End)

From Wesley Ivan Hurt, Dec 29 2016: (Start)

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

a(2*k) = 5*k-3, a(2*k-1) = 5*k-4. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2-2*sqrt(5)/5)*Pi/10 + log(phi)/sqrt(5), where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021

E.g.f.: 3 + ((5*x - 9/2)*exp(x) - (3/2)*exp(-x))/2. - David Lovler, Aug 23 2022

Maple

A047216:=n->(10*n-3*(-1)^n-9)/4: seq(A047216(n), n=1..100); # Wesley Ivan Hurt, Dec 29 2016

Mathematica

Select[Range[0, 200], MemberQ[{1, 2}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)

Prog

(PARI) a(n)=(n-1)\2*5+2-n%2 \\ Charles R Greathouse IV, Dec 22 2011
(Magma) [(10*n-3*(-1)^n-9)/4 : n in [1..100]]; // Wesley Ivan Hurt, Dec 29 2016

Crossrefs

Cf. A001622, A047209, A047211, A047212, A176059.

Sequence in context: A369648 A221847 A283766 * A244970 A242330 A039568

Adjacent sequences: A047213 A047214 A047215 * A047217 A047218 A047219

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved