The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A001850

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A001850

Central Delannoy numbers: a(n) = Sum_{k=0..n} C(n,k)*C(n+k,k).
(history; published version)

#479 by Michael De Vlieger at Wed Sep 18 16:33:19 EDT 2024

STATUS

reviewed

approved

#478 by Stefano Spezia at Wed Sep 18 15:13:07 EDT 2024

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proposed

reviewed

#477 by Peter Bala at Wed Sep 18 12:38:44 EDT 2024

STATUS

editing

proposed

#476 by Peter Bala at Wed Sep 18 12:37:21 EDT 2024

FORMULA

a(n-1) + a(n+1) = A241023(n) for n >= 1. - Peter Bala, Sep 18 2024

#475 by Peter Bala at Wed Sep 18 08:11:05 EDT 2024

FORMULA

a(n) + a(n+1) = A241023(n). - Peter Bala, Sep 18 2024

CROSSREFS

Cf. A008288, bisection of A026003, A027618, A047665, A052141, A084773, A152250, A109980, A000129, A078057, A241023, A243949.

STATUS

approved

editing

#474 by Michael De Vlieger at Sat Aug 10 21:39:25 EDT 2024

STATUS

reviewed

approved

#473 by Michel Marcus at Sat Aug 10 16:44:37 EDT 2024

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proposed

reviewed

#472 by Andrew Howroyd at Sat Aug 10 16:27:26 EDT 2024

STATUS

editing

proposed

#471 by Andrew Howroyd at Sat Aug 10 16:26:19 EDT 2024

COMMENTS

So, as a special case of Dmitry Zaitsev's Dec 10 2015 comment on A008288, a(n) is the number of points in Z^n that are L1 (Manhattan) distance <= n from any given point. (??) These terms occur in the crystal ball sequences: a(n) here is the n-th term in the sequence for the n-dimensional cubic lattice. See A008288 for a list of crystal ball sequences (rows or columns of A008288). - Shel Kaphan, Dec 26 2022

Discussion

Sat Aug 10

16:27

Andrew Howroyd: No worries, we will just undo.

#470 by Michel Marcus at Sat Aug 10 01:00:07 EDT 2024

STATUS

proposed

editing

Discussion

Sat Aug 10

11:38

Don Knuth: i apologize for misreading ... I was thinking of Manhattan distance on Z^2 (which is the dimension used by taxi drivers in Manhattan, and I never heard the phrase applied to other dimensions), so I missed the n in Z^n