A105395 A simple "Fractal Jump Sequence" (FJS).

1, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1, 7, 1, 1

Offset: 1

Author

Eric Angelini, May 01 2005

Keywords

• base
• easy
• nonn

Comments

See A105397 for definition of Fractal Jump Sequence.

a(n+2) = the digital root of the n-th centered hexagonal number (A003215). - Colin Barker, Jan 30 2015

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Cf. A003215, A105397, A003215.

Programs

Mathematica

PadRight[{1}, 100, {7, 1, 1}] (* Paolo Xausa, Jul 17 2024 *)

PARI

Vec(-x*(2*x+1)*(3*x^2-x+1)/((x-1)*(x^2+x+1))  + O(x^100)) \\ Colin Barker, Jan 30 2015

Formula

a(n) = a(n-3) for n>4. - Colin Barker, Jan 30 2015

G.f.: -x*(2*x+1)*(3*x^2-x+1) / ((x-1)*(x^2+x+1)). - Colin Barker, Jan 30 2015