The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A373608

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A373608

Number of (binary) heaps of length n whose element set equals [k], where k is chosen so as to maximize this number.
(history; published version)

#19 by Alois P. Heinz at Fri Jun 14 11:11:06 EDT 2024

STATUS

editing

approved

#18 by Alois P. Heinz at Fri Jun 14 11:11:03 EDT 2024

CROSSREFS

Row maxima of A373451.

Cf. A002869, A373451.

STATUS

approved

editing

#17 by OEIS Server at Thu Jun 13 14:28:37 EDT 2024

LINKS

Alois P. Heinz, <a href="/A373608/b373608_1.txt">Table of n, a(n) for n = 0..495</a>

#16 by Alois P. Heinz at Thu Jun 13 14:28:37 EDT 2024

STATUS

editing

approved

Discussion

Thu Jun 13

14:28

OEIS Server: Installed first b-file as b373608.txt.

#15 by Alois P. Heinz at Wed Jun 12 20:39:11 EDT 2024

FORMULA

a(n) = max({ A373451(n,k) : 0 <= k <= n }).

#14 by Alois P. Heinz at Wed Jun 12 20:33:56 EDT 2024

EXAMPLE

a(7) = 502: 5141123, 5141132, 5241113, 5241123, 5241131, 5241132, 5241133, ..., 5553421, 5554123, 5554132, 5554213, 5554231, 5554312, 5554321 (with k=5).

#13 by Alois P. Heinz at Wed Jun 12 20:28:49 EDT 2024

EXAMPLE

a(6) = 92: 413112, 423111, 423112, 423113, 423121, 423122, 423123, ..., 443421, 444123, 444132, 444213, 444231, 444312, 444321 (with k=4).

#12 by Alois P. Heinz at Wed Jun 12 20:22:14 EDT 2024

EXAMPLE

(The examples use max-heaps.)

#11 by Alois P. Heinz at Wed Jun 12 20:21:32 EDT 2024

EXAMPLE

a(4) = 7: 3121, 3211, 3212, 3221, 3231, 3312, 3321 (with k=3).

#10 by Alois P. Heinz at Wed Jun 12 20:20:25 EDT 2024

COMMENTS

These heaps may contain repeated elements. Their element sets are gap-free and contain 1 (if nonempty).