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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

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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.

E.g.f.: (4*cosh(x) + exp(-x/2) * (sqrt(3)*sin(sqrt(3)*x/2) - cos(sqrt(3)*x/2)) + sinh(x)) / 3. - Amiram Eldar, Jan 19 2026

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. A115356, A171182.

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

URL: https://oeis.org/A115357

⇱ A115357 - OEIS