A304580 Period 16: repeat 1,8,3,6,5,4,7,2,9,0,7,2,5,4,3,6.

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

Offset

1,2

Comments

Repeating sequences of alternating odd and even single digits that in pairs sum to 9, 11 or 7. Note that 1836547290725436 = 20202020197979796 / 11.

Links

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

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

Formula

From Colin Barker, May 28 2018: (Start)

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

a(n) = a(n-2) - a(n-8) + a(n-10) for n > 10.

(End)

Mathematica

LinearRecurrence[{0, 1, 0, 0, 0, 0, 0, -1, 0, 1}, {1, 8, 3, 6, 5, 4, 7, 2, 9, 0}, 100] (* or *) PadRight[{}, 100, {1, 8, 3, 6, 5, 4, 7, 2, 9, 0, 7, 2, 5, 4, 3, 6}] (* Harvey P. Dale, Sep 28 2021 *)

Prog

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

Crossrefs

Cf. A172423, A172430, A304583.

Sequence in context: A005601 A321098 A308741 * A304583 A104697 A228211

Adjacent sequences: A304577 A304578 A304579 * A304581 A304582 A304583

Keyword

nonn,easy

Author

Halfdan Skjerning, May 15 2018

Status

approved