[seqfan] Partitions and Offsets
Melvin M Peralta
melvinmperalta at gmail.com
Thu Jan 5 21:52:46 CET 2017
Not a new sequence, but maybe a simple way of finding new connections
between sequences.
Partition a sequence into blocks of size n with offset i, then find the sum
of each block.
An elementary example: partition the non-negative integers into blocks of
size 2 with offset 1 and find the sum - this yields the positive odd
integers.
This can be extended to any number of sequences and any number of blocks
and offsets.
Some cursory experimentation with the Fibonacci numbers (A000045) revealed
connections:
A025169 appears to be the sum of the partitions of A000045 with blocks of
size 3 and offset 2.
A002878 (for n > 1) appears to be the sum of the partitions of A000045 with
blocks of size 4 and offset 2.
A100545 appears to be the sum of the partitions of A00045 with blocks of
size 5 and offset 2.
I wonder if other connections can be made, and at the very least this might
be an avenue for lots of recreational exploration
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