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A125235
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Triangle with the partial column sums of the octagonal numbers.
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1
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| "Partial column sums" means the octagonal numbers are the 1st column, the 2nd column are the partial sums of the 1st column, the 3rd column are the partial sums of the 2nd etc.
Row sums of are 1, 9, 31, 81, 187, 405, 847 = 7*(2^n-1)-6*n. - R. J. Mathar, Sep 06 2011
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REFERENCES
| Albert H. Beiler, Recreations in the Theory of Numbers, Dover (1966), p. 189.
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FORMULA
| T(n,1) = A000567(n).
T(n,k) = T(n-1,k-1) + T(n-1,k), k>1.
T(n,2) = A002414(n-1).
T(n,3) = A002419(n-2).
T(n,4) = A051843(n-4).
T(n,5) = A027810(n-6).
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EXAMPLE
| 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;
...
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CROSSREFS
| Cf. A000567, A002414, A002419, A051843, A027810, A125232 - A125234.
Sequence in context: A013615 A103884 A103883 * A183892 A019432 A002173
Adjacent sequences: A125232 A125233 A125234 * A125236 A125237 A125238
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 24 2006
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