A329003 Numbers k such that the coefficient of x^k in the expansion of Product_{j>=2} (1 - x^Fibonacci(j)) is zero.

3, 5, 6, 9, 10, 15, 16, 17, 21, 25, 26, 27, 28, 32, 34, 35, 37, 41, 42, 43, 44, 45, 46, 50, 52, 53, 56, 57, 60, 61, 63, 67, 68, 69, 70, 71, 72, 73, 74, 75, 79, 81, 82, 85, 86, 91, 92, 93, 98, 99, 102, 103, 105, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120

Offset: 1

Author

Ilya Gutkovskiy, Nov 01 2019

Keywords

• nonn

Comments

Numbers k such that number of partitions of k into an even number of distinct Fibonacci parts equals number of partitions of k into an odd number of distinct Fibonacci parts (1 counted as single Fibonacci number).

Positions of 0's in A093996.

Complement of A151661.

Crossrefs

Cf. A000045, A000119, A003107, A090864, A093996, A151661.

Programs

Mathematica

Flatten[Position[Rest[CoefficientList[Series[Product[(1 - x^Fibonacci[j]), {j, 2, 21}], {x, 0, 130}], x]], 0]]