OFFSET
1,1
COMMENTS
A strong Schreier set is a subset of the positive integers with cardinality less than the minimum element in the set (see Chu link).
Each term k of 2*A371176 can be put into a one-to-one correspondence with a strong Schreier set by interpreting the 1-based position of the ones in the binary expansion of k (where position 1 corresponds to the least significant bit) as the elements of the corresponding strong Schreier set.
Arranging the elements in each set in decreasing order results in the sets being listed in lexicographical order (see example). Cf. A373579 for the elements arranged in increasing order.
The number of sets having maximum element m is A000045(m-1).
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000 (rows 1..2261 of the triangle, flattened).
Alistair Bird, Jozef Schreier, Schreier sets and the Fibonacci sequence, Out Of The Norm blog, May 13 2012.
Hùng Việt Chu, The Fibonacci Sequence and Schreier-Zeckendorf Sets, Journal of Integer Sequences, Vol. 22 (2019), Article 19.6.5.
FORMULA
T(n,k) = A373345(n,k) + 1.
EXAMPLE
Triangle begins:
Corresponding
(this sequence)
---------------------------------------------------------
1 2 10 {2}
2 4 100 {3}
3 8 1000 {4}
4 12 1100 {4, 3}
5 16 10000 {5} Sets are
6 20 10100 {5, 3} lexicographically
7 24 11000 {5, 4} ordered
8 32 100000 {6}
9 36 100100 {6, 3}
10 40 101000 {6, 4}
11 48 110000 {6, 5}
12 56 111000 {6, 5, 4}
...
MATHEMATICA
Join[{{2}}, Map[Reverse[PositionIndex[Reverse[IntegerDigits[#, 2]]][1]] &, Select[Range[4, 400, 4], DigitCount[#, 2, 1] < IntegerExponent[#, 2] + 1 &]]]
CROSSREFS
KEYWORD
nonn,tabf,base,easy
AUTHOR
Paolo Xausa, Jun 09 2024
STATUS
approved