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

%I A122930 #12 Jun 29 2025 02:09:20
%S A122930 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,
%T A122930 10,18,30,40,104,0,714,13,16,30,45,80,104,273,0,1870,21,26,48,75,120,
%U A122930 208,273,714,0,4895,34,42,78,120,200,312,546,714,1870,0,12816
%N A122930 Triangular array read by rows, based on the Zeckendorf expansion of n and containing the golden rectangle sequence A001629.
%H A122930 Amiram Eldar, <a href="/A122930/b122930.txt">Table of n, a(n) for n = 1..210</a> (rows n=1..20, flattened)
%e A122930 The array begins:
%e A122930   1
%e A122930   0 2
%e A122930   1 0 6
%e A122930   1 2 0 15
%e A122930   2 2 6 0 40
%e A122930   3 4 6 15 0 104
%e A122930   5 6 12 15 40 0 273
%e A122930 Row five is:
%e A122930   2 2 6 0 40
%e A122930 because the values
%e A122930   1 2 3 5 8 in Zeckendorf's expansion occur
%e A122930   2 1 2 0 5 times for natural numbers 8 through 12.
%t A122930 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 *)
%Y A122930 Cf. A001629, A014417, A122931.
%K A122930 nonn,tabl
%O A122930 1,3
%A A122930 _Alford Arnold_, Sep 20 2006
%E A122930 More terms from _Amiram Eldar_, Jun 28 2025