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Search: id:A008867
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| A008867 |
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Triangle of truncated triangular numbers: k-th term in n-th row is number of dots in hexagon of sides k, n-k, k, n-k, k, n-k. |
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+0
2
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| 1, 3, 3, 6, 7, 6, 10, 12, 12, 10, 15, 18, 19, 18, 15, 21, 25, 27, 27, 25, 21, 28, 33, 36, 37, 36, 33, 28, 36, 42, 46, 48, 48, 46, 42, 36, 45, 52, 57, 60, 61, 60, 57, 52, 45, 55, 63, 69, 73, 75, 75, 73, 69, 63, 55, 66, 75, 82, 87, 90, 91, 90, 87, 82, 75, 66, 78, 88, 96, 102, 106, 108
(list; table; graph; listen)
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OFFSET
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2,2
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COMMENT
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Closely related to A109439. The current sequence is made of truncated triangular numbers, the latter gives the full description. Both can help to build a cube with layers perpendicular to the great diagonal. E.g.: 15,18,19,18,15 in A008867 is a truncation of the lesser triangular numbers of 1,3,6,10,15,18,19,18,15,10,6,3,1 in A109439. - M. Dauchez (mdzzdm(AT)yahoo.fr), Sep 02 2005
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LINKS
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J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (Abstract, pdf, ps).
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MAPLE
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n*(n-3)/2 - k^2+k*n+1;
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CROSSREFS
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Row sums are in A005900.
Cf. A109439.
Sequence in context: A117775 A021301 A016652 this_sequence A003879 A078565 A026926
Adjacent sequences: A008864 A008865 A008866 this_sequence A008868 A008869 A008870
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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njas, J. H. Conway and R. K. Guy
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