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Search: id:A079273
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| A079273 |
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Octo numbers (a polygonal sequence): 5n^2-6n+2, or (n-1)^2 + (2n-1)^2. |
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+0
1
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| 1, 10, 29, 58, 97, 146, 205, 274, 353, 442, 541, 650, 769, 898, 1037, 1186, 1345, 1514, 1693, 1882, 2081, 2290, 2509, 2738, 2977, 3226, 3485, 3754, 4033, 4322, 4621, 4930, 5249, 5578, 5917, 6266, 6625, 6994, 7373, 7762, 8161, 8570, 8989, 9418, 9857, 10306
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n+1) = a(n)+10n-1, and n+a(n) is always congruent to 2 mod 10 (notice pattern of final digits). a(n)= the n-th hex number (3n^2-3n+1) added to the (2n-2)nd triangular number (2n^2-3n+1). The formula for the n-th octo number can be written as (2n-1)^2 + (n-1)^2; compare to formula for n-th octagonal number, n(3n-2)= (2n-1)^2 - (n-1)^2.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World Of Mathematics. (on hex numbers)
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EXAMPLE
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a(4)=58 because 58 dots can be arranged into a simple octagonal pattern with 4 dots on each side, its rows from top to bottom containing 4,5,6,7,7,7,7,6,5, and 4 dots respectively. The pattern is similar to the pattern for hex numbers (see link), with the exception that while the n-th hex figure has only 1 row of length 2n-1 dots (the maximum length) in the center, the n-th octo figure has n such rows.
a(4) = 58:
.. O O O O
. O O O O O
.O O O O O O
O O O O O O O
O O O O O O O
O O O O O O O
O O O O O O O
.O O O O O O
. O O O O O
.. O O O O
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CROSSREFS
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Cf. A000217 (triangular numbers), A000567 (octagonal numbers), A003215 (hex numbers).
Sequence in context: A098751 A009771 A068197 this_sequence A048469 A048772 A055850
Adjacent sequences: A079270 A079271 A079272 this_sequence A079274 A079275 A079276
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Matthew Vandermast (ghodges14(AT)comcast.net), Feb 06 2003
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