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Ordered Fibonomial coefficients (A144712) which are not Fibonacci numbers (A000045).
2

%I #12 Oct 10 2023 05:32:21

%S 6,15,40,60,104,260,273,714,1092,1820,1870,4641,4895,12376,12816,

%T 19635,33552,83215,85085,87841,136136,229970,352440,582505,602070,

%U 1493064,1514513,1576239,3994320,4126648,6324552,10803704,16776144,26791505

%N Ordered Fibonomial coefficients (A144712) which are not Fibonacci numbers (A000045).

%C Complement of A144712 with A000045.

%C Not surprisingly, many are Golden rectangle numbers (A001654).

%H Robert G. Wilson v, <a href="/A171159/b171159.txt">Table of n, a(n) for n = 1..54</a>

%t f[n_, k_] := Product[Fibonacci[n - j + 1]/Fibonacci[j], {j, k}]; fibQ[n_] := (Fibonacci@ Round@ Log[ GoldenRatio, n*Sqrt@5] == n); Take[ Select[ Union@ Flatten@ Table[ f[n, i], {n, 0, 19}, {i, 0, Floor[n/2]}], ! fibQ@# &], 34]

%Y Cf. A000045, A010048, A144712, A001654.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Dec 04 2009