[seqfan] Re: Link between A053726 and A193773.

hv at crypt.org hv at crypt.org
Thu Apr 4 13:24:50 CEST 2024


I'd be inclined to add a form of this:
  It is clear that N is in A053726 exactly when A193776(N-1) > 1.
as a formula on A053726, and the same formula as a comment on A193776.

Does it need more commentary than that?

Hugo

Allan Wechsler <acwacw at gmail.com> wrote:
:The number of representations of n as 2XY - X - Y (1 <= X <= Y) is recorded
:in oeis.org/A193773.
:
:The list of numbers of the form 2KL - K - L + 1, (2 <= K <= L) is in
:oeis.org/A053726. (These are "flag numbers", where N stars can be arranged
:on a flag in a K-by-L rectangle with a (K-1)-by-(L-1) rectangle
:interleaved. The current flag of the USA shows that 50 is a flag number,
:with K = 6 and L = 5.)
:
:It is clear that N is in A053726 exactly when A193776(N-1) > 1.
:
:Neither sequence currently acknowledges its relationship to the other. I'd
:like to add cross-links and commentary, but I don't want to clutter up both
:entries. Does anyone have advice on how to add this connection gracefully?
:
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