The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A006566 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A006566

Dodecahedral numbers: a(n) = n*(3*n - 1)*(3*n - 2)/2.
(history; published version)

#126 by Michael De Vlieger at Tue Jan 09 08:47:29 EST 2024

STATUS

reviewed

approved

#125 by Michel Marcus at Tue Jan 09 04:26:10 EST 2024

STATUS

proposed

reviewed

#124 by Amiram Eldar at Tue Jan 09 03:00:35 EST 2024

STATUS

editing

proposed

#123 by Amiram Eldar at Tue Jan 09 03:00:23 EST 2024

FORMULA

Sum_{n>=1} 1/a(n) = A295421. - _From _Amiram Eldar_, Jan 09 2024: (Start)

Sum_{n>=1} 1/a(n) = (sqrt(3)*Pi - 3*log(3))/2 (A295421).

Sum_{n>=1} (-1)^(n+1)/a(n) = (12*log(2) - sqrt(3)*Pi)/3. (End)

STATUS

proposed

editing

#122 by Amiram Eldar at Tue Jan 09 01:08:23 EST 2024

STATUS

editing

proposed

#121 by Amiram Eldar at Tue Jan 09 00:49:05 EST 2024

CROSSREFS

Cf. A027907, A035006, A060544, A093485, A124388, A228887, A228888, A295421.

#120 by Amiram Eldar at Tue Jan 09 00:39:22 EST 2024

LINKS

Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.

Ed Pegg Jr, <a href="/A006566/a006566.jpg">Dodecahedral 2024</a>.

#119 by Amiram Eldar at Tue Jan 09 00:38:54 EST 2024

COMMENTS

Schlaefli symbol for this polyhedron: {5,3}.

CROSSREFS

Cf. A027907, A093485, A124388, A228887, A228888, A295421.

#118 by Amiram Eldar at Tue Jan 09 00:36:21 EST 2024

FORMULA

Sum_{n>=1} 1/a(n) = A295421. - Amiram Eldar, Jan 09 2024

CROSSREFS

Cf. A027907, A228887, A228888, A295421.

STATUS

approved

editing

#117 by Alois P. Heinz at Thu Jan 04 14:59:04 EST 2024

STATUS

proposed

approved