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Nine steps forward, eight steps back.
1

%I #6 Aug 25 2024 13:08:56

%S 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,

%T 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,

%U 8,7,6,5,4,5,6,7,8,9,10,11,12,13,12,11,10

%N Nine steps forward, eight steps back.

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

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

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

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

%t Table[Sum[(-1)^Floor[(2 i - 2)/17], {i, n}], {n, 0, 100}]

%t 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 *)

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

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

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

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

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

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

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

%K nonn,easy

%O 0,3

%A _Wesley Ivan Hurt_, May 31 2017