A138189 Sequence built on pattern (1,-even,-even) beginning 1,-2,-2.

1, -2, -2, 1, -4, -4, 1, -6, -6, 1, -8, -8, 1, -10, -10, 1, -12, -12, 1, -14, -14, 1, -16, -16, 1, -18, -18, 1, -20, -20, 1, -22, -22, 1, -24, -24, 1, -26, -26, 1, -28, -28, 1, -30, -30, 1, -32, -32, 1, -34, -34, 1, -36, -36, 1, -38, -38, 1, -40, -40

Offset: 0

Author

Paul Barry, Mar 04 2008

Keywords

• easy
• sign

Comments

Partial sums of A138188.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Crossrefs

Cf. A110090, A138188.

Programs

Magma

b:= [n le 2 select 0 else Abs(2*Self(n-1) -Self(n-2)) -Self(n-1)-1: n in [1..120]];
A138189:= func< n | -b[n+3] >;
[A138189(n): n in [0..100]]; // G. C. Greubel, Jun 16 2021

Mathematica

Join[{1},Riffle[Flatten[{-2#,-2#}&/@Range[25]],1,3]] (* Harvey P. Dale, Nov 02 2011 *)

Sage

@CachedFunction
def A138189(n):
    if (n%3==0): return 1
    elif (n%3==1): return -2*(n//3 +1)
    else: return -2*(n//3 +1)
[A138189(n) for n in (0..100)] # G. C. Greubel, Jun 16 2021

Formula

G.f.: (1 -2*x -2*x^2 -x^3)/(1 -2*x^3 +x^6).

From G. C. Greubel, Jun 16 2021: (Start)

a(n) = -b(n+3), where b(n) = abs(2*b(n-1) - b(n-2)) - b(n-1) - 1 and b(1) = b(2) = 0.

a(n) = 1 if (n mod 3) = 0, -2*(floor(n/3) + 1) if (n mod 3) = 1 or (n mod 3) = 2. (End)