A287794 Nine steps forward, eight steps back.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 12, 11, 10

Offset: 0

Author

Wesley Ivan Hurt, May 31 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A008611 (one step back, two steps forward).

Cf. A058207 (three steps forward, two steps back).

Cf. A260644 (four steps forward, three steps back).

Cf. A271800 (five steps forward, four steps back).

Cf. A271859 (six steps forward, five steps back).

Cf. A287655 (seven steps forward, six steps back).

Cf. A287793 (eight steps forward, seven steps back).

Programs

Maple

a:=n->add((-1)^floor((2*i-2)/17), i=1..n): seq(a(n), n=0..200);

Mathematica

Table[Sum[(-1)^Floor[(2 i - 2)/17], {i, n}], {n, 0, 100}]
LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1},{0,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1},100] (* Harvey P. Dale, Aug 25 2024 *)

Formula

a(n) = Sum_{i=1..n} (-1)^floor((2*i-2)/17).

a(n) = a(n-1) + a(n-17) - a(n-18) for n > 17.