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

Author

Alford Arnold, Sep 20 2006

Keywords

• nonn
• tabl

Examples

			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.
		

Links

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

Crossrefs

Cf. A001629, A014417, A122931.

Programs

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 *)

Extensions

More terms from Amiram Eldar, Jun 28 2025