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A054967 Numbers that are congruent to {0, 1, 9} mod 10. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A086446 A168042 A045522 * A227801 A048031 A048013

Adjacent sequences:  A054964 A054965 A054966 * A054968 A054969 A054970

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, May 24 2000

STATUS

approved

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Last modified January 17 18:28 EST 2018. Contains 297829 sequences.