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Search: id:A125750
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| A125750 |
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A Moessner triangle using (1,3,5...). |
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+0
3
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| 1, 3, 5, 10, 19, 11, 42, 89, 64, 19, 216, 498, 415, 160, 29, 1320, 3254, 3023, 1385, 335, 41, 9360, 24372, 24640, 12803, 3745, 623, 55, 75600, 206100, 223116, 127799, 42938, 8750, 1064, 71, 685440, 1943568, 2227276, 1380076, 516201, 122010, 18354, 1704
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Right border of the triangle = A028387, left border = A007680
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REFERENCES
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J. H. Conway and R. K. Guy, "The Book of Numbers", Springer-Verlag, 1996, p. 63-64.
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LINKS
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Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Jun 17 2007, Table of n, a(n) for n = 1..78
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FORMULA
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Using "Moessner's Magic" (Conway and Guy, p. 63-64), (C.f. A125714), we circle the 1,3,6,10...(-th) terms in the sequence (1,3,5,7...) and take partial sums of the remaining terms, making row 2. Circle the terms in row 2 one place offset to the left of row 1 terms, then take partial sums. Continue with analogous operations for succeeding rows. The triangle = leftmost circled terms in each row.
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EXAMPLE
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Circling the 1,3,6...(-th) terms in the sequence (1,3,5,7...), we get A018387: (1, 5, 11, 19, 29...). Taking partial sums of the remaining terms, we get (3, 10, 19, 32...) in row 2 and we circle 3 and 19. In row 3 we circle the 10.
First few rows of the triangle are:
1;
3, 5;
10, 19, 11;
42, 89, 64, 19;
216, 498, 415, 160, 29;
...
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CROSSREFS
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Cf. A125714, A125751, A125752.
Adjacent sequences: A125747 A125748 A125749 this_sequence A125751 A125752 A125753
Sequence in context: A107232 A134522 A001445 this_sequence A018168 A084321 A133999
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 06 2006
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EXTENSIONS
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More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Jun 17 2007
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