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

1,4

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

Paolo Xausa, Table of n, a(n) for n = 1..1000

Victor Kelly, Animated GIF

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

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

Mathematica

A337879[n_] := Fibonacci[n + 1 - 2*Quotient[n + 1, 3]]; Array[A337879, 60] (* Paolo Xausa, Jul 05 2026 *)
(* Alternative: *)
LinearRecurrence[{0, 0, 1, 0, 0, 1}, {1, 1, 1, 2, 1, 2}, 60] (* Paolo Xausa, Jul 05 2026 *)

Crossrefs

Cf. A000045, A001519, A001906, A008611.

Sequence in context: A119994 A029167 A161103 * A147301 A108380 A361231

Adjacent sequences: A337876 A337877 A337878 * A337880 A337881 A337882

Keyword

nonn,easy,changed

Author

Victor Kelly, Sep 22 2020

Extensions

More terms from Alois P. Heinz, Sep 29 2020

Status

approved