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

Author

Paul Barry, Jan 21 2006

Keywords

• easy
• nonn

Comments

Diagonal sums of number triangle A115356.

Links

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

Crossrefs

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

Cf. A115356.

Programs

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 *)

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.