A304583 Period 18: repeat 1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8.

1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8, 1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4

Offset

1,2

Comments

Repeating sequences of alternating odd and even single digits that in pairs sum to 9 or 11. Note that 183654729092745638 = 2020202020020202018 / 11.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

From Colin Barker, May 28 2018: (Start)

G.f.: x*(1 + 9*x + 11*x^2 + 9*x^3 + 11*x^4 + 9*x^5 + 11*x^6 + 9*x^7 + 11*x^8 + 8*x^9) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 + x^3 + x^6)).

a(n) = -a(n-1) + a(n-9) + a(n-10) for n > 10.

(End)

Mathematica

PadRight[{}, 120, {1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 9, 2, 7, 4, 5, 6, 3, 8}] (* Harvey P. Dale, Feb 10 2024 *)

Prog

(PARI) Vec(x*(1 + 9*x + 11*x^2 + 9*x^3 + 11*x^4 + 9*x^5 + 11*x^6 + 9*x^7 + 11*x^8 + 8*x^9) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 + x^3 + x^6)) + O(x^50)) \\ Colin Barker, May 28 2018

Crossrefs

Cf. A172423, A172430, A304580.

Sequence in context: A321098 A308741 A304580 * A104697 A228211 A010522

Adjacent sequences: A304580 A304581 A304582 * A304584 A304585 A304586

Keyword

nonn,easy

Author

Halfdan Skjerning, May 15 2018

Status

approved