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Sequence of the Day for November 3

A119258: Triangle read by rows
n   ≥   0: T  (n, 0) = T  (n, n) = 1
and for
0 < k < n: T  (n, k ) = 2 T  (n  −  1, k  −  1) + T  (n  −  1, k )
.
1
1 1
1 3 1
1 5 7 1
1 7 17 15 1
1 9 31 49 31 1
1 11 49 111 129 63 1

This sequence is a Pascal-like triangle (see Pascal triangle). It appears naturally in combinatorics, topology, representation theory, computer science and numerical analysis. The natural formula for the terms seems to depend heavily on the context in which they appear, but it is not hard to show by hand that all these formulae satisfy the defining recursive formula.



The following is in the <noinclude> ... </noinclude> section.

For more details about today's Sequence of the Day, see {{Sequence of the Day for November 3}}.

Guidelines for selecting the Sequence of the Day

  • These are not rules. But if they were rules, they would only be enforced by the honor system.
  • Whenever practical, the Sequence of the Day should bear some relation either to the calendar date (hint: browse arXiv e-prints by date) or to some recent newsworthy event.
  • The write-up should be brief and not require advanced mathematical knowledge to understand.
  • Positive preference given to sequences with keyword:nice.
  • No special preference for sequences with keyword:core.
  • Negative preference for sequences with keyword:uned or keyword:less. However, it is perfectly acceptable to polish up an uned sequence just prior to featuring.
  • Each OEIS contributor should get at least one opportunity to choose the Sequence of the Day.
  • The chooser ought not choose a sequence they have authored. But one they have edited heavily is perfectly acceptable.
  • Ideally this will be changed each day at 0:00 per the OEIS Wiki clock. Each Sequence of the Day should be up for at least 22 hours but not more than 26 hours.
  • There shouldn't be a big, heavy, bureaucratic apparatus to administer this feature.