A337879 a(n) is the length of the n-th line segment to draw the squares of the Fibonacci spiral without lifting the pencil, including superpositions.

1, 1, 1, 2, 1, 2, 3, 2, 3, 5, 3, 5, 8, 5, 8, 13, 8, 13, 21, 13, 21, 34, 21, 34, 55, 34, 55, 89, 55, 89, 144, 89, 144, 233, 144, 233, 377, 233, 377, 610, 377, 610, 987, 610, 987, 1597, 987, 1597, 2584, 1597, 2584, 4181, 2584, 4181, 6765, 4181, 6765, 10946

Offset: 1

Author

Victor Kelly, Sep 22 2020

Keywords

• nonn
• easy

Comments

To draw the Fibonacci squares without lifting your pencil, go a(n) units and turn 90 degrees (same direction every time), and so on (see the animation).

As an array read by rows, with two columns, in which column 1 lists three copies of every nonzero term of A001906 in nondecreasing order, and the column 2 lists 1 together with three copies of every term > 1 of A001519 in nondecreasing order. - Omar E. Pol, Sep 29 2020

Links

• Victor Kelly, Animated GIF
• Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,0,1).

Crossrefs

Cf. A000045, A001519, A001906, A008611.

Formula

a(n) = Fibonacci(A008611(n+2)). - David A. Corneth, Sep 28 2020

G.f.: -x*(x^5+x^3+x^2+x+1)/(x^6+x^3-1). - Alois P. Heinz, Sep 29 2020

a(n) = a(n-3) + a(n-6) for n > 6. - Jinyuan Wang, Sep 30 2020

Extensions

More terms from Alois P. Heinz, Sep 29 2020