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Search: id:A035313
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| A035313 |
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(Largest) diagonal of the Zorach additive triangle. |
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+0
7
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| 1, 3, 9, 26, 66, 154, 346, 771, 1726, 3887, 8768, 19700, 43890, 96717, 210665, 453893, 968903, 2053260, 4328489, 9093971, 19068611, 39943689, 83628399, 175018523, 366081209, 765102907, 1597315656, 3330380593, 6933810145
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Comment from Philippe Lallouet (philip.lallouet(AT)wanadoo.fr), Apr 22 2007: (Start)
Starting with 1, smallest sequence for which:
all its terms a1(n).............................. 1,3,9,26,66
all terms of first differences a2(n)=a1(n+1)-a1(n) 2,6,17,40
all terms of second differences a3(n)=a2(n+1)-a2(n) 4,11,23
...
all terms of (1+i)th differences ai(n)=ai-1(n+1)-ai-1(n)
are different for any n and any i (End)
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LINKS
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A. C. Zorach, Additive triangle
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EXAMPLE
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Start with 1; 2 is the next, then add 1+2 to get 3, then 4 is next, then 4+2=6 and 6+3 is 9, then 5 is not next because 5+4=9 and 9 was already used, so 7 is next...which ultimately generates 26 in the final column...
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CROSSREFS
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Cf. A035311, A035312, A035358.
Sequence in context: A119851 A119825 A037260 this_sequence A055293 A034531 A048470
Adjacent sequences: A035310 A035311 A035312 this_sequence A035314 A035315 A035316
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Alexander C. Zorach (cazort(AT)udel.edu)
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EXTENSIONS
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More terms from Christian G. Bower (bowerc(AT)usa.net) and Dean Hickerson dean.hickerson(AT)yahoo.com
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