A054967 Numbers that are congruent to {0, 1, 9} mod 10.

0, 1, 9, 10, 11, 19, 20, 21, 29, 30, 31, 39, 40, 41, 49, 50, 51, 59, 60, 61, 69, 70, 71, 79, 80, 81, 89, 90, 91, 99, 100, 101, 109, 110, 111, 119, 120, 121, 129, 130, 131, 139, 140, 141, 149, 150, 151, 159, 160, 161, 169, 170, 171, 179, 180, 181, 189, 190, 191, 199

Offset

1,3

Comments

Numbers with last digit 0, 1, or 9. - Wesley Ivan Hurt, Jun 14 2016

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

G.f.: x^2*(x^2+8*x+1)/((x-1)^2*(x^2+x+1)). - Robert Israel, Feb 23 2016

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. - Vincenzo Librandi, Feb 24 2016

From Wesley Ivan Hurt, Jun 14 2016: (Start)

a(n) = (30*n-30+21*cos(2*n*Pi/3)+7*sqrt(3)*sin(2*n*Pi/3))/9.

a(3k) = 10k-1, a(3k-1) = 10k-9, a(3k-2) = 10k-10. (End)

Maple

seq(seq(10*i+j, j=[0, 1, 9]), i=0..30); # Robert Israel, Feb 23 2016

Mathematica

Select[Range[0, 200], MemberQ[{0, 1, 9}, Mod[#, 10]] &] (* or *) LinearRecurrence[{1, 0, 1, -1}, {0, 1, 9, 10}, 60] (* Vincenzo Librandi, Feb 24 2016 *)

Prog

(Magma) [n: n in [0..200] | n mod 10 in [0, 1, 9]]; // Vincenzo Librandi, Feb 24 2016

Crossrefs

Cf. A047523.

Sequence in context: A168042 A342147 A045522 * A227801 A048031 A048013

Adjacent sequences: A054964 A054965 A054966 * A054968 A054969 A054970

Keyword

nonn,easy

Author

Henry Bottomley, May 24 2000

Status

approved