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Search: id:A125235
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| A125235 |
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Triangle, partial column sums of the octagonal numbers. |
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+0
2
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| 1, 8, 1, 21, 9, 1, 40, 30, 10, 1, 65, 70, 40, 11, 1, 96, 135, 110, 51, 12, 1, 133, 231, 245, 161, 63, 13, 1, 176, 364, 476, 406, 224, 76, 14, 1, 225, 540, 840, 882, 630, 300, 90, 15, 1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Left border = octagonal numbers, (A000567: 1, 8, 21, 40, 65,...); then columns going to the right = A002414, A002419, A051843, A027810. Analogous triangles for the pentagonal numbers = A125232; hexagonal, A125233; heptagonal, A125234. Row sums of A125235 = 1, 9, 31, 81, 187, 405, 847.
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REFERENCES
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Albert H. Beiler, "Recreations in the Theory of Numbers", Dover, 1966, p. 189.
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FORMULA
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Let the left border = A000567, the octagonal numbers; then T(n,k) = (n-1,k) + (n-1,k-1), k>1.
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EXAMPLE
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First few rows of the triangle are:
1;
8, 1;
21, 9, 1;
40, 30, 10, 1;
65, 70, 40, 11, 1;
96, 135, 110, 51, 12, 1;
...
(5,3) = 110 = 40 + 70 = (4,3) + (4,2).
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CROSSREFS
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Cf. A000567, A002414, A002419, A051843, A027810, A125232, A125233, A125234.
Sequence in context: A013615 A103884 A103883 this_sequence A019432 A138505 A002173
Adjacent sequences: A125232 A125233 A125234 this_sequence A125236 A125237 A125238
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 24 2006
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