A122930 Triangular array read by rows, based on the Zeckendorf expansion of n and containing the golden rectangle sequence A001629.

1, 0, 2, 1, 0, 6, 1, 2, 0, 15, 2, 2, 6, 0, 40, 3, 4, 6, 15, 0, 104, 5, 6, 12, 15, 40, 0, 273, 8, 10, 18, 30, 40, 104, 0, 714, 13, 16, 30, 45, 80, 104, 273, 0, 1870, 21, 26, 48, 75, 120, 208, 273, 714, 0, 4895, 34, 42, 78, 120, 200, 312, 546, 714, 1870, 0, 12816

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..210 (rows n=1..20, flattened)

Example

The array begins:
  1
  0 2
  1 0 6
  1 2 0 15
  2 2 6 0 40
  3 4 6 15 0 104
  5 6 12 15 40 0 273
Row five is:
  2 2 6 0 40
because the values
  1 2 3 5 8 in Zeckendorf's expansion occur
  2 1 2 0 5 times for natural numbers 8 through 12.

Mathematica

seq[rownum_] := Plus @@@ SplitBy[(#*Fibonacci[Range[2, Length[#] + 1]]) & /@ Reverse /@ IntegerDigits[FromDigits /@ Select[Tuples[{0, 1}, rownum], SequenceCount[#, {1, 1}] == 0 &]], Length] // Flatten; seq[11] (* Amiram Eldar, Jun 28 2025 *)

Crossrefs

Cf. A001629, A014417, A122931.

Sequence in context: A157982 A119275 A129462 * A396744 A364303 A364518

Adjacent sequences: A122927 A122928 A122929 * A122931 A122932 A122933

Keyword

nonn,tabl

Author

Alford Arnold, Sep 20 2006

Extensions

More terms from Amiram Eldar, Jun 28 2025

Status

approved