A115357 Period 6: repeat [1,1,1,0,2,0].

1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0

Offset

0,5

Comments

Diagonal sums of number triangle A115356.

Links

Table of n, a(n) for n=0..71.

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

Formula

G.f.: (1+2*x+2*x^2)/(1+x-x^3-x^4).

a(n) = -a(n-1)+a(n-3)+a(n-4).

a(n) = -cos(2*Pi*n/3+Pi/6)/sqrt(3)+sin(2*Pi*n/3+Pi/6)/3+(-1)^n/2+5/6.

Sequence shifted right by 2 is additive with a(p^e) = 1 if p = 2 or 3, 0 otherwise.

Mathematica

PadRight[{}, 120, {1, 1, 1, 0, 2, 0}] (* or *) LinearRecurrence[{-1, 0, 1, 1}, {1, 1, 1, 0}, 120] (* Harvey P. Dale, Jan 28 2015 *)

Crossrefs

Cf. A171182. [From Juri-Stepan Gerasimov, Dec 04 2009]

Cf. A115356.

Sequence in context: A280750 A280748 A117454 * A171182 A333806 A340832

Adjacent sequences: A115354 A115355 A115356 * A115358 A115359 A115360

Keyword

easy,nonn

Author

Paul Barry, Jan 21 2006

Status

approved