A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.[1] The centered octagonal numbers are the same as the odd square numbers.[2] Thus, the nth odd square number and tth centered octagonal number is given by the formula
The first few centered octagonal numbers are[2]
Calculating Ramanujan's tau function on a centered octagonal number yields an odd number, whereas for any other number the function yields an even number.[2]
is the number of 2x2 matrices with elements from 0 to n that their determinant is twice their permanent.
See also
[edit]References
[edit]- ^ Teo, Boon K.; Sloane, N. J. A. (1985), "Magic numbers in polygonal and polyhedral clusters" (PDF), Inorganic Chemistry, 24 (26): 4545–4558, doi:10.1021/ic00220a025.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A016754 (Odd squares: (2n-1)^2. Also centered octagonal numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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Well, that’s interesting to know that Psilotum nudum are known as whisk ferns. Psilotum nudum is the commoner species of the two. While the P. flaccidum is a rare species and is found in the tropical islands. Both the species are usually epiphytic in habit and grow upon tree ferns. These species may also be terrestrial and grow in humus or in the crevices of the rocks.
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